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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#不定積分"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>不定積分</span> </div> </a> <ul id="toc-不定積分-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目錄" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="開/收內容一覽" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">開/收內容一覽</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">積分</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="去睇另一種語文嘅文章。有92種語言版本。" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-92" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">92種語言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%8C%A0%E1%88%AB%E1%89%83%E1%88%9A" title="አጠራቃሚ – 阿姆哈拉文" lang="am" hreflang="am" data-title="አጠራቃሚ" data-language-autonym="አማርኛ" data-language-local-name="阿姆哈拉文" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Integraci%C3%B3n" title="Integración – 阿拉貢文" lang="an" hreflang="an" data-title="Integración" data-language-autonym="Aragonés" data-language-local-name="阿拉貢文" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%83%D8%A7%D9%85%D9%84" title="تكامل – 阿拉伯文" lang="ar" hreflang="ar" data-title="تكامل" data-language-autonym="العربية" data-language-local-name="阿拉伯文" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Integraci%C3%B3n" title="Integración – 阿斯圖里亞文" lang="ast" hreflang="ast" data-title="Integración" data-language-autonym="Asturianu" data-language-local-name="阿斯圖里亞文" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0nteqral" title="İnteqral – 亞塞拜然文" lang="az" hreflang="az" data-title="İnteqral" data-language-autonym="Azərbaycanca" data-language-local-name="亞塞拜然文" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%86%D8%AA%D9%82%D8%B1%D8%A7%D9%84" title="انتقرال – South Azerbaijani" lang="azb" hreflang="azb" data-title="انتقرال" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 巴什客爾文" lang="ba" hreflang="ba" data-title="Интеграл" data-language-autonym="Башҡортса" data-language-local-name="巴什客爾文" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D0%BD%D1%82%D1%8D%D0%B3%D1%80%D0%B0%D0%BB" title="Інтэграл – 白俄羅斯文" lang="be" hreflang="be" data-title="Інтэграл" data-language-autonym="Беларуская" data-language-local-name="白俄羅斯文" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 保加利亞文" lang="bg" hreflang="bg" data-title="Интеграл" data-language-autonym="Български" data-language-local-name="保加利亞文" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AF%E0%A7%8B%E0%A6%97%E0%A6%9C%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3" title="যোগজীকরণ – 孟加拉文" lang="bn" hreflang="bn" data-title="যোগজীকরণ" data-language-autonym="বাংলা" data-language-local-name="孟加拉文" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Integral" title="Integral – 波士尼亞文" lang="bs" hreflang="bs" data-title="Integral" data-language-autonym="Bosanski" data-language-local-name="波士尼亞文" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle mw-list-item" title="正文"><a href="https://ca.wikipedia.org/wiki/Integraci%C3%B3" title="Integració – 加泰羅尼亞文" lang="ca" hreflang="ca" data-title="Integració" data-language-autonym="Català" data-language-local-name="加泰羅尼亞文" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%95%D9%88%D8%A7%D9%88%DA%A9%D8%A7%D8%B1%DB%8C" title="تەواوکاری – 索拉尼庫爾德文" lang="ckb" hreflang="ckb" data-title="تەواوکاری" data-language-autonym="کوردی" data-language-local-name="索拉尼庫爾德文" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Integr%C3%A1l" title="Integrál – 捷克文" lang="cs" hreflang="cs" data-title="Integrál" data-language-autonym="Čeština" data-language-local-name="捷克文" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 楚瓦什文" lang="cv" hreflang="cv" data-title="Интеграл" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什文" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Integryn" title="Integryn – 威爾斯文" lang="cy" hreflang="cy" data-title="Integryn" data-language-autonym="Cymraeg" data-language-local-name="威爾斯文" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Integral" title="Integral – 德文" lang="de" hreflang="de" data-title="Integral" data-language-autonym="Deutsch" data-language-local-name="德文" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/%C4%B0ntegral" title="İntegral – Zazaki" lang="diq" hreflang="diq" data-title="İntegral" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dtp mw-list-item"><a href="https://dtp.wikipedia.org/wiki/Ponompuuvan" title="Ponompuuvan – 中部杜順文" lang="dtp" hreflang="dtp" data-title="Ponompuuvan" data-language-autonym="Kadazandusun" data-language-local-name="中部杜順文" class="interlanguage-link-target"><span>Kadazandusun</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BF%CE%BA%CE%BB%CE%AE%CF%81%CF%89%CE%BC%CE%B1" title="Ολοκλήρωμα – 希臘文" lang="el" hreflang="el" data-title="Ολοκλήρωμα" data-language-autonym="Ελληνικά" data-language-local-name="希臘文" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Integral" title="Integral – 英文" lang="en" hreflang="en" data-title="Integral" data-language-autonym="English" data-language-local-name="英文" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Integralo" title="Integralo – 世界文" lang="eo" hreflang="eo" data-title="Integralo" data-language-autonym="Esperanto" data-language-local-name="世界文" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Integraci%C3%B3n" title="Integración – 西班牙文" lang="es" hreflang="es" data-title="Integración" data-language-autonym="Español" data-language-local-name="西班牙文" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Integraal" title="Integraal – 愛沙尼亞文" lang="et" hreflang="et" data-title="Integraal" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu badge-Q17437796 badge-featuredarticle mw-list-item" title="正文"><a href="https://eu.wikipedia.org/wiki/Integral" title="Integral – 巴斯克文" lang="eu" hreflang="eu" data-title="Integral" data-language-autonym="Euskara" data-language-local-name="巴斯克文" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%AA%DA%AF%D8%B1%D8%A7%D9%84" title="انتگرال – 波斯文" lang="fa" hreflang="fa" data-title="انتگرال" data-language-autonym="فارسی" data-language-local-name="波斯文" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Integraali" title="Integraali – 芬蘭文" lang="fi" hreflang="fi" data-title="Integraali" data-language-autonym="Suomi" data-language-local-name="芬蘭文" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Int%C3%A9gration_(math%C3%A9matiques)" title="Intégration (mathématiques) – 法文" lang="fr" hreflang="fr" data-title="Intégration (mathématiques)" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Integral" title="Integral – 加里西亞文" lang="gl" hreflang="gl" data-title="Integral" data-language-autonym="Galego" data-language-local-name="加里西亞文" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B8%E0%AA%82%E0%AA%95%E0%AA%B2%E0%AA%A8" title="સંકલન – 古吉拉特文" lang="gu" hreflang="gu" data-title="સંકલન" data-language-autonym="ગુજરાતી" data-language-local-name="古吉拉特文" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Chit-f%C3%BBn-ho%CC%8Dk" title="Chit-fûn-ho̍k – 客家話" lang="hak" hreflang="hak" data-title="Chit-fûn-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="客家話" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%A0%D7%98%D7%92%D7%A8%D7%9C" title="אינטגרל – 希伯來文" lang="he" hreflang="he" data-title="אינטגרל" data-language-autonym="עברית" data-language-local-name="希伯來文" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A4%BE%E0%A4%95%E0%A4%B2%E0%A4%A8" title="समाकलन – 北印度文" lang="hi" hreflang="hi" data-title="समाकलन" data-language-autonym="हिन्दी" data-language-local-name="北印度文" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Integral" title="Integral – 克羅埃西亞文" lang="hr" hreflang="hr" data-title="Integral" data-language-autonym="Hrvatski" data-language-local-name="克羅埃西亞文" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Entegrasyon_(matematik)" title="Entegrasyon (matematik) – 海地文" lang="ht" hreflang="ht" data-title="Entegrasyon (matematik)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地文" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Integr%C3%A1l" title="Integrál – 匈牙利文" lang="hu" hreflang="hu" data-title="Integrál" data-language-autonym="Magyar" data-language-local-name="匈牙利文" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BB%D5%B6%D5%BF%D5%A5%D5%A3%D6%80%D5%A1%D5%AC" title="Ինտեգրալ – 亞美尼亞文" lang="hy" hreflang="hy" data-title="Ինտեգրալ" data-language-autonym="Հայերեն" data-language-local-name="亞美尼亞文" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Integral" title="Integral – 印尼文" lang="id" hreflang="id" data-title="Integral" data-language-autonym="Bahasa Indonesia" data-language-local-name="印尼文" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Integralo" title="Integralo – 伊多文" lang="io" hreflang="io" data-title="Integralo" data-language-autonym="Ido" data-language-local-name="伊多文" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Heildun" title="Heildun – 冰島文" lang="is" hreflang="is" data-title="Heildun" data-language-autonym="Íslenska" data-language-local-name="冰島文" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Integrale" title="Integrale – 義大利文" lang="it" hreflang="it" data-title="Integrale" data-language-autonym="Italiano" data-language-local-name="義大利文" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%98%E1%83%9C%E1%83%A2%E1%83%94%E1%83%92%E1%83%A0%E1%83%90%E1%83%9A%E1%83%98" title="ინტეგრალი – 喬治亞文" lang="ka" hreflang="ka" data-title="ინტეგრალი" data-language-autonym="ქართული" data-language-local-name="喬治亞文" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Integral" title="Integral – 卡拉卡爾帕克文" lang="kaa" hreflang="kaa" data-title="Integral" data-language-autonym="Qaraqalpaqsha" data-language-local-name="卡拉卡爾帕克文" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 哈薩克文" lang="kk" hreflang="kk" data-title="Интеграл" data-language-autonym="Қазақша" data-language-local-name="哈薩克文" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%A2%E1%9E%B6%E1%9F%86%E1%9E%84%E1%9E%8F%E1%9F%81%E1%9E%80%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9B" title="អាំងតេក្រាល – 高棉文" lang="km" hreflang="km" data-title="អាំងតេក្រាល" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="高棉文" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%A8%E0%B3%81%E0%B2%95%E0%B2%B2%E0%B2%A8%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಅನುಕಲನಶಾಸ್ತ್ರ – 坎那達文" lang="kn" hreflang="kn" data-title="ಅನುಕಲನಶಾಸ್ತ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="坎那達文" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%81%EB%B6%84" title="적분 – 韓文" lang="ko" hreflang="ko" data-title="적분" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/%C3%8Entegral" title="Întegral – 庫爾德文" lang="ku" hreflang="ku" data-title="Întegral" data-language-autonym="Kurdî" data-language-local-name="庫爾德文" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 吉爾吉斯文" lang="ky" hreflang="ky" data-title="Интеграл" data-language-autonym="Кыргызча" data-language-local-name="吉爾吉斯文" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Integrale" title="Integrale – 拉丁文" lang="la" hreflang="la" data-title="Integrale" data-language-autonym="Latina" data-language-local-name="拉丁文" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Integral" title="Integral – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Integral" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Integralas" title="Integralas – 立陶宛文" lang="lt" hreflang="lt" data-title="Integralas" data-language-autonym="Lietuvių" data-language-local-name="立陶宛文" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Integr%C4%81lis" title="Integrālis – 拉脫維亞文" lang="lv" hreflang="lv" data-title="Integrālis" data-language-autonym="Latviešu" data-language-local-name="拉脫維亞文" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%AE%E0%B4%BE%E0%B4%95%E0%B4%B2%E0%B4%A8%E0%B4%82" title="സമാകലനം – 馬來亞拉姆文" lang="ml" hreflang="ml" data-title="സമാകലനം" data-language-autonym="മലയാളം" data-language-local-name="馬來亞拉姆文" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 蒙古文" lang="mn" hreflang="mn" data-title="Интеграл" data-language-autonym="Монгол" data-language-local-name="蒙古文" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A4%B2%E0%A4%A8" title="संकलन – 馬拉地文" lang="mr" hreflang="mr" data-title="संकलन" data-language-autonym="मराठी" data-language-local-name="馬拉地文" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kamiran" title="Kamiran – 馬來文" lang="ms" hreflang="ms" data-title="Kamiran" data-language-autonym="Bahasa Melayu" data-language-local-name="馬來文" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/L-Integral" title="L-Integral – 馬爾他文" lang="mt" hreflang="mt" data-title="L-Integral" data-language-autonym="Malti" data-language-local-name="馬爾他文" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%84%E1%80%BA%E1%80%90%E1%80%AE%E1%80%82%E1%80%9B%E1%80%B1%E1%80%B8%E1%80%9B%E1%80%BE%E1%80%84%E1%80%BA%E1%80%B8" title="အင်တီဂရေးရှင်း – 緬甸文" lang="my" hreflang="my" data-title="အင်တီဂရေးရှင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="緬甸文" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Integraal" title="Integraal – 荷蘭文" lang="nl" hreflang="nl" data-title="Integraal" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Integral" title="Integral – 耐諾斯克挪威文" lang="nn" hreflang="nn" data-title="Integral" data-language-autonym="Norsk nynorsk" data-language-local-name="耐諾斯克挪威文" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Integrasjon" title="Integrasjon – 巴克摩挪威文" lang="nb" hreflang="nb" data-title="Integrasjon" data-language-autonym="Norsk bokmål" data-language-local-name="巴克摩挪威文" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Integracion" title="Integracion – 奧克西坦文" lang="oc" hreflang="oc" data-title="Integracion" data-language-autonym="Occitan" data-language-local-name="奧克西坦文" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Wajjummaa" title="Wajjummaa – 奧羅莫文" lang="om" hreflang="om" data-title="Wajjummaa" data-language-autonym="Oromoo" data-language-local-name="奧羅莫文" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ca%C5%82ka" title="Całka – 波蘭文" lang="pl" hreflang="pl" data-title="Całka" data-language-autonym="Polski" data-language-local-name="波蘭文" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D9%B9%DB%8C%DA%AF%D8%B1%D9%84" title="انٹیگرل – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انٹیگرل" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Integral" title="Integral – 葡萄牙文" lang="pt" hreflang="pt" data-title="Integral" data-language-autonym="Português" data-language-local-name="葡萄牙文" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Integral%C4%83" title="Integrală – 羅馬尼亞文" lang="ro" hreflang="ro" data-title="Integrală" data-language-autonym="Română" data-language-local-name="羅馬尼亞文" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 俄文" lang="ru" hreflang="ru" data-title="Интеграл" data-language-autonym="Русский" data-language-local-name="俄文" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Intiggrali" title="Intiggrali – 西西里文" lang="scn" hreflang="scn" data-title="Intiggrali" data-language-autonym="Sicilianu" data-language-local-name="西西里文" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Integral" title="Integral – 蘇格蘭文" lang="sco" hreflang="sco" data-title="Integral" data-language-autonym="Scots" data-language-local-name="蘇格蘭文" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Integral" title="Integral – 塞爾維亞克羅埃西亞文" lang="sh" hreflang="sh" data-title="Integral" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞爾維亞克羅埃西亞文" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Integral" title="Integral – Simple English" lang="en-simple" hreflang="en-simple" data-title="Integral" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Integr%C3%A1l" title="Integrál – 斯洛伐克文" lang="sk" hreflang="sk" data-title="Integrál" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克文" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Integral" title="Integral – 斯洛維尼亞文" lang="sl" hreflang="sl" data-title="Integral" data-language-autonym="Slovenščina" data-language-local-name="斯洛維尼亞文" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Integrali" title="Integrali – 阿爾巴尼亞文" lang="sq" hreflang="sq" data-title="Integrali" data-language-autonym="Shqip" data-language-local-name="阿爾巴尼亞文" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 塞爾維亞文" lang="sr" hreflang="sr" data-title="Интеграл" data-language-autonym="Српски / srpski" data-language-local-name="塞爾維亞文" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Integral" title="Integral – 巽他文" lang="su" hreflang="su" data-title="Integral" data-language-autonym="Sunda" data-language-local-name="巽他文" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Integral" title="Integral – 瑞典文" lang="sv" hreflang="sv" data-title="Integral" data-language-autonym="Svenska" data-language-local-name="瑞典文" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Ukamilishaji_(hisabati)" title="Ukamilishaji (hisabati) – 史瓦希里文" lang="sw" hreflang="sw" data-title="Ukamilishaji (hisabati)" data-language-autonym="Kiswahili" data-language-local-name="史瓦希里文" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%95%E0%AF%88%E0%AE%AF%E0%AF%80%E0%AE%9F%E0%AF%81" title="தொகையீடு – 坦米爾文" lang="ta" hreflang="ta" data-title="தொகையீடு" data-language-autonym="தமிழ்" data-language-local-name="坦米爾文" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B4%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B9%8C" title="ปริพันธ์ – 泰文" lang="th" hreflang="th" data-title="ปริพันธ์" data-language-autonym="ไทย" data-language-local-name="泰文" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0ntegral" title="İntegral – 土耳其文" lang="tr" hreflang="tr" data-title="İntegral" data-language-autonym="Türkçe" data-language-local-name="土耳其文" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – 韃靼文" lang="tt" hreflang="tt" data-title="Интеграл" data-language-autonym="Татарча / tatarça" data-language-local-name="韃靼文" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Інтеграл – 烏克蘭文" lang="uk" hreflang="uk" data-title="Інтеграл" data-language-autonym="Українська" data-language-local-name="烏克蘭文" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%DA%A9%D8%A7%D9%85%D9%84" title="تکامل – 烏都文" lang="ur" hreflang="ur" data-title="تکامل" data-language-autonym="اردو" data-language-local-name="烏都文" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Integral" title="Integral – 烏茲別克文" lang="uz" hreflang="uz" data-title="Integral" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="烏茲別克文" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Integral" title="Integral – 威尼斯文" lang="vec" hreflang="vec" data-title="Integral" data-language-autonym="Vèneto" data-language-local-name="威尼斯文" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%C3%ADch_ph%C3%A2n" title="Tích phân – 越南文" lang="vi" hreflang="vi" data-title="Tích phân" data-language-autonym="Tiếng Việt" data-language-local-name="越南文" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Riveye" title="Riveye – 瓦隆文" lang="wa" hreflang="wa" data-title="Riveye" data-language-autonym="Walon" data-language-local-name="瓦隆文" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%A7%AF%E5%88%86" title="积分 – 中文" lang="zh" hreflang="zh" data-title="积分" data-language-autonym="中文" data-language-local-name="中文" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Chek-hun" title="Chek-hun – 閩南語" lang="nan" hreflang="nan" data-title="Chek-hun" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="閩南語" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q80091#sitelinks-wikipedia" title="改跨語言拎" class="wbc-editpage">改拎</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="空間名"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" 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vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">閱讀設定</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移去側欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">收埋</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">出自維基百科，自由嘅百科全書</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="yue" dir="ltr"><p><b>積分</b>（<em lang="en">integration</em>；<a href="/wiki/Wikipedia:%E7%B2%B5%E6%96%87%E6%8B%BC%E9%9F%B3" title="Wikipedia:粵文拼音">粵拼</a>：<span class="plainlinks" style="display:inline-block"><a rel="nofollow" class="external text" href="http://yue.forvo.com/word/yue/積分/#yue"><span>zik<span class="Jpingtone">1</span> fan<span class="Jpingtone">1</span></span></a></span>；香港俗稱 in），係<a href="/w/index.php?title=%E9%AB%98%E7%AD%89%E6%95%B8%E5%AD%B8&action=edit&redlink=1" class="new" title="高等數學 (無呢版)">高等數學</a>裏頭嘅一個核心概念，亦都係<a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a>同<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數學分析</a>嘅基礎之一。可以分爲<a href="/wiki/%E5%AE%9A%E7%A9%8D%E5%88%86" class="mw-redirect" title="定積分">定積分</a>同<a href="/w/index.php?title=%E4%B8%8D%E5%AE%9A%E7%A9%8D%E5%88%86&action=edit&redlink=1" class="new" title="不定積分 (無呢版)">不定積分</a>兩種。 </p><p>好多時都會用積分嚟求曲線面積等嘅資料。 </p> <div class="mw-heading mw-heading2"><h2 id="定積分"><span id=".E5.AE.9A.E7.A9.8D.E5.88.86"></span>定積分</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A9%8D%E5%88%86&action=edit&section=1" title="編輯小節: 定積分"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Integral_example.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Integral_example.png/220px-Integral_example.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Integral_example.png/330px-Integral_example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Integral_example.png/440px-Integral_example.png 2x" data-file-width="1400" data-file-height="1400" /></a><figcaption>用圖表示定積分</figcaption></figure> <p>如果有一個任意<a href="/wiki/%E5%87%BD%E6%95%B8" title="函數">函數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle f(x)}"></span> ，佢由 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> 至 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> 之間嘅定積分就會係噉樣表示： </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=\int _{a}^{b}f(x)\,dx.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=\int _{a}^{b}f(x)\,dx.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11a5b51d8aaf33e93499510f7c8771ea84d72e5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.056ex; height:6.343ex;" alt="{\displaystyle I=\int _{a}^{b}f(x)\,dx.}"></span> </p><p>而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> 就係圖示喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/094f824655138f6b11d96a0da32e7f0716ba6959" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.416ex; height:2.509ex;" alt="{\displaystyle y=0}"></span> 至 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2311a6a75c54b0ea085a381ba472c31d59321514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.672ex; height:2.843ex;" alt="{\displaystyle y=f(x)}"></span> 範圍入面，喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> 至 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> 之間， <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 軸係正數嘅面積減去 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 軸係負數嘅面積。 </p> <div class="mw-heading mw-heading2"><h2 id="不定積分"><span id=".E4.B8.8D.E5.AE.9A.E7.A9.8D.E5.88.86"></span>不定積分</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A9%8D%E5%88%86&action=edit&section=2" title="編輯小節: 不定積分"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="navigation" class="navbox" aria-labelledby="應用數學" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" 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href="/wiki/%E5%A0%B4_(%E6%95%B8%E5%AD%B8)" class="mw-redirect mw-disambig" title="場 (數學)">場</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學">組合數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%9C%96%E8%AB%96" title="圖論">圖論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%A2%E6%95%A3%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="離散幾何學">離散幾何學</a></div></td><td class="navbox-image" rowspan="8" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Aizerman2d.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/150px-Aizerman2d.jpg" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/225px-Aizerman2d.jpg 1.5x, 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href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" title="實分析">實分析</a>同<a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">複分析</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%96%93%E8%B7%9D" title="間距">間距</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%84%A1%E7%AA%AE%E7%9B%A1" title="無窮盡">無窮盡</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%84%A1%E7%AA%AE%E5%B0%8F%E9%87%8F" title="無窮小量">無窮小量</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E6%95%B8%E5%88%97" class="mw-redirect" title="數列">數列</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%AD%90%E6%95%B8%E5%88%97" title="子數列">子數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A2%9E%E6%B8%9B%E6%95%B8%E5%88%97" title="增減數列">增減數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%83%9D%E6%B0%8F%E6%95%B8%E5%88%97" title="郝氏數列">郝氏數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BF%9D%E8%A5%BF%E5%A5%B4-%E8%8F%AF%E5%AF%A6%E6%96%AF%E5%AE%9A%E7%90%86" title="保西奴-華實斯定理">保西奴-華實斯定理</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%87%BD%E6%95%B8" title="函數">函數</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%80%A3%E7%BA%8C%E5%87%BD%E6%95%B8" title="連續函數">連續函數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A5%B5%E9%99%90_(%E5%87%BD%E6%95%B8)" title="極限 (函數)">極限</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%80%BC%E8%BF%91%E7%90%86%E8%AB%96" title="逼近理論">逼近理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%B3%9B%E5%87%BD%E5%88%86%E6%9E%90" title="泛函分析">泛函分析</a>（<a href="/wiki/%E8%AE%8A%E5%88%86%E6%B3%95" title="變分法">變分法</a>）</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="微分" scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%BE%AE%E5%88%86" title="微分">微分</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程">微分方程</a>（<a href="/wiki/%E5%B8%B8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="常微分方程">常</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%81%8F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="偏微分方程">偏</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="隨機微分方程">隨機</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%A4%87%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="複微分方程">複</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95" title="微分幾何">微分幾何</a></div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a class="mw-selflink selflink">積分</a>（<a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%A9%8D%E5%88%86" title="黎曼積分">黎曼積分</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A9%8D%E5%88%86%E6%96%B9%E7%A8%8B" title="積分方程">積分方程</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%9A%E5%85%83%E5%BE%AE%E7%A9%8D%E5%88%86" title="多元微積分">多元微積分</a>（<a href="/wiki/%E5%90%91%E9%87%8F%E5%BE%AE%E7%A9%8D%E5%88%86" title="向量微積分">向量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BC%B5%E9%87%8F%E5%BE%AE%E7%A9%8D%E5%88%86" title="張量微積分">張量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%9A%E9%87%8D%E7%A9%8D%E5%88%86" title="多重積分">多重積分</a>）</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">第啲分析</div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%A4%9A%E9%87%8D%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="多重線性代數">多線代數</a>（<a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%90%91%E9%87%8F%E7%A9%BA%E9%96%93" title="向量空間">向量空間</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BC%B5%E9%87%8F" title="張量">張量</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%8B%95%E6%85%8B%E7%B3%BB%E7%B5%B1" title="動態系統">動態系統</a>（<a href="/wiki/%E6%B7%B7%E6%B2%8C%E7%90%86%E8%AB%96" title="混沌理論">混沌理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AB%96" title="控制理論">控制理論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%AB%A7%E6%B3%A2%E5%88%86%E6%9E%90" title="諧波分析">諧波分析</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%80%BC%E5%88%86%E6%9E%90" title="數值分析">數值分析</a></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E5%AD%B8" title="運算數學">運算數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%AE%97%E9%82%8F%E8%BC%AF" title="運算邏輯">運算邏輯</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%87%AA%E5%8B%95%E6%A9%9F%E7%90%86%E8%AB%96" title="自動機理論">自動機理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95" title="演算法">演算法</a>（<a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95%E5%88%86%E6%9E%90" title="演算法分析">分析</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%B3%87%E8%A8%8A%E7%90%86%E8%AB%96" title="資訊理論">資訊理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AF%86%E7%A2%BC%E5%AD%B8" title="密碼學">密碼學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E8%AB%96" title="運算數論">運算數論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E9%81%8B%E7%AE%97" title="科學運算">科學運算</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%BB%E8%85%A6%E4%BB%A3%E6%95%B8" title="電腦代數">電腦代數</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%9A%A8%E6%A9%9F%E8%AE%8A%E6%95%B8" title="隨機變數">隨機變數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E9%81%8E%E7%A8%8B" title="隨機過程">隨機過程</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%A6%AC%E5%8F%AF%E5%A4%AB%E9%8F%88" title="馬可夫鏈">馬可夫鏈</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%BE%AE%E7%A9%8D%E5%88%86" title="隨機微積分">隨機微積分</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%B1%BA%E7%AD%96%E8%AB%96" title="決策論">決策論</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學">統計學</a>（<a href="/wiki/%E6%8F%8F%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" title="描述統計學">描述</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%8E%A8%E8%AB%96%E7%B5%B1%E8%A8%88%E5%AD%B8" title="推論統計學">推論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%9C%80%E4%BD%B3%E5%8C%96" title="最佳化">最佳化</a>（<a href="/wiki/%E7%B7%9A%E6%80%A7%E8%A6%8F%E5%8A%83" title="線性規劃">線性</a>同<a href="/wiki/%E9%9D%9E%E7%B7%9A%E6%80%A7%E8%A6%8F%E5%8A%83" title="非線性規劃">非線性</a>規劃）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%B6%93%E6%BF%9F%E5%AD%B8" title="數理經濟學">數理經濟學</a><span 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