{"id":197281,"date":"2022-06-22T09:30:00","date_gmt":"2022-06-22T04:00:00","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=197281"},"modified":"2022-09-03T18:20:38","modified_gmt":"2022-09-03T12:50:38","slug":"maths-integration-formula-explained-with-examples-cbse-class-12-maths","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-integration-formula-explained-with-examples-cbse-class-12-maths\/","title":{"rendered":"Integration Formula Explained With Examples | CBSE Class 12 Maths"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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0;font-family:&quot;Merriweather&quot;,serif;font-size:0.404531em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Integration Formula Explained With Examples | CBSE Class 12 Maths<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:14.07767%;height:9.38511%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f4dec856-9f7d-4700-9fda-b1445fe06f03\">\n<div style=\"position:absolute;width:100%;height:100.00004%;left:0%;top:-0.00002%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png\" alt=\"Aakash Icon Blue PNG\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png 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class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-a915dfba-7f79-49e1-9218-90b449d1a624\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10.jpg\" alt=\"10\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/10-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:6.79612%;width:75.97087%;height:9.54693%;opacity:1\">\n<div id=\"anim-66886e75-7934-45f0-bdd0-5b99a0047f8e\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.33547%, 0px, 0)\">\n<div id=\"anim-a8306510-088b-45fb-8362-6b4ec7ed65c9\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a141344e-eda4-4961-8739-1b4375fc19cc\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6389776357827476% 0.6389776357827476% 0.6389776357827476% 0.6389776357827476% \/ 3.389830508474576% 3.389830508474576% 3.389830508474576% 3.389830508474576%\" id=\"el-444eed05-ec34-4d0a-95db-c0405443acb3\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.5025559105431311% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">In mathematics, there are two types of integrals:<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:24.59547%;width:75.97087%;height:4.53074%;opacity:1\">\n<div id=\"anim-b2c9ac83-6377-487c-ac23-7d2e2e0ad041\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.01598%, 0px, 0)\">\n<div id=\"anim-b8eb5655-f9bd-4651-a262-10c69ce1a565\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-61831262-a5b8-4e59-8b1e-7e90a656e98b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6389776357827476% 0.6389776357827476% 0.6389776357827476% 0.6389776357827476% \/ 7.142857142857142% 7.142857142857142% 7.142857142857142% 7.142857142857142%\" id=\"el-c16f7bd9-abc3-4e7b-bf89-02ca94895bc8\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.5025559105431311% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Type 1: Definite Integral<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:12.37864%;top:34.30421%;width:75.97087%;height:9.54693%;opacity:1\">\n<div id=\"anim-e9ea6be6-f91e-464c-9c80-6cec75f5f180\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-116.29393%, 0px, 0)\">\n<div id=\"anim-51cb92b7-04e4-438b-ac12-f12e2e1a2f80\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-c6eea9c4-ca43-4b18-9695-8d224f676976\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6389776357827476% 0.6389776357827476% 0.6389776357827476% 0.6389776357827476% \/ 3.389830508474576% 3.389830508474576% 3.389830508474576% 3.389830508474576%\" id=\"el-c4d2a94d-0e2c-4d9f-82b6-852616259c08\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.5025559105431311% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">The upper and lower limits are provided in this integral.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:calc(9.95146% - 5px);top:calc(51.2945% - 5px);width:calc(80.09709% + 10px);height:calc(32.03883% + 10px);opacity:1\">\n<div style=\"top:0;left:0;right:0;bottom:0;width:100%;height:100%;position:absolute;border-width:5px 5px 5px 5px;border-color:rgba(255,255,255,1);border-style:solid;border-radius:6.0606060606060606% 6.0606060606060606% 6.0606060606060606% 6.0606060606060606% \/ 10.1010101010101% 10.1010101010101% 10.1010101010101% 10.1010101010101%;pointer-events:initial;display:block;z-index:0\" class=\"mask\" id=\"el-ba4cda17-5f70-41ff-9b48-70bbb82d44c5\">\n<div style=\"position:absolute;width:100%;height:296.29635%;left:0%;top:-70.0354%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-2-1.png\" alt=\"Integration-formulas-2-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-2-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-2-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-2-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-2-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"cf8413e8-8638-4f52-ab50-24cfd17449fa\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-94472f9b-207b-49c7-8029-439cacbae8e4\",\"keyframes\":{\"transform\":[\"translate3d(-114.77988%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-bd5d3164-cda5-48cf-a36a-36b1d1336168\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-7774671a-3e04-427b-ae4d-9a7058b60448\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-00d85270-3018-4092-8edd-6fc859995840\",\"keyframes\":{\"transform\":[\"translate3d(-114.77988%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-d6dfadd5-ef33-412f-a236-1a84872e8e76\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-072b4989-3d4b-4cb1-ac88-ab1259bb1605\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#27322a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-cd101a26-d51a-4226-8358-4e2a445ad593\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/5-4.jpg\" alt=\"5 (4)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/5-4.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/5-4-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/5-4-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/5-4-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:11.65049%;width:77.18447%;height:4.53074%;opacity:1\">\n<div id=\"anim-94472f9b-207b-49c7-8029-439cacbae8e4\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-114.77988%, 0px, 0)\">\n<div id=\"anim-bd5d3164-cda5-48cf-a36a-36b1d1336168\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-7774671a-3e04-427b-ae4d-9a7058b60448\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 7.142857142857142% 7.142857142857142% 7.142857142857142% 7.142857142857142%\" id=\"el-fca7fa23-9bd7-42ac-a7f5-7a5a8a198e26\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.49465408805031463% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Type 2: Indefinite Integral<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:25.24272%;width:77.18447%;height:14.23948%;opacity:1\">\n<div id=\"anim-00d85270-3018-4092-8edd-6fc859995840\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-114.77988%, 0px, 0)\">\n<div id=\"anim-d6dfadd5-ef33-412f-a236-1a84872e8e76\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-072b4989-3d4b-4cb1-ac88-ab1259bb1605\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 2.272727272727273% 2.272727272727273% 2.272727272727273% 2.272727272727273%\" id=\"el-4b5f0eb3-be14-4786-ae8b-1f09365cf0f1\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.49465408805031463% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Indefinite integrals are those that have no upper or lower limitations.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:calc(4.36893% - 5px);top:calc(47.24919% - 5px);width:calc(91.01942% + 10px);height:calc(25.72816% + 10px);opacity:1\">\n<div style=\"top:0;left:0;right:0;bottom:0;width:100%;height:100%;position:absolute;border-width:5px 5px 5px 5px;border-color:rgba(255,255,255,1);border-style:solid;border-radius:5.333333333333334% 5.333333333333334% 5.333333333333334% 5.333333333333334% \/ 12.578616352201259% 12.578616352201259% 12.578616352201259% 12.578616352201259%;pointer-events:initial;display:block;z-index:0\" class=\"mask\" id=\"el-991eddf9-cd5c-4050-8df4-1a0dba57104a\">\n<div style=\"position:absolute;width:118.9675%;height:498.81544%;left:-8.89628%;top:-106.81068%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-3-1.png\" alt=\"Integration-formulas-3-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-3-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-3-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-3-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-3-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 41vh, 91vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"62040cee-6b44-4e7c-8291-abf31c7b8d78\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-7113ca78-9b7b-4a2e-82e9-de937363f713\",\"keyframes\":[{\"offset\":0,\"transform\":\"translate3d(0, -707.778%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.29,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.45,\"transform\":\"translate3d(0, -199.0271736%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.61,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.71,\"transform\":\"translate3d(0, -67.6635768%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.8,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.85,\"transform\":\"translate3d(0, -25.409230200000003%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.92,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.96,\"transform\":\"translate3d(0, -11.0413368%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":1,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"}],\"delay\":0,\"duration\":1300,\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#284893\">\n<div 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type=\"application\/json\">[{\"selector\":\"#anim-d7161efd-bf2e-4612-a0b3-9dab4f433f8c\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#061527\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-63d4aef1-c5c6-4ecd-91b4-1e0eb5d3b4e5\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/27.jpg\" alt=\"27\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/27.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/27-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/27-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/27-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-image:linear-gradient(0.5turn, rgba(0,0,0,0) 40%, rgba(0,0,0,0.5) 100%)\"><\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-image:linear-gradient(0.5turn, rgba(0,0,0,0) 40%, rgba(0,0,0,0.5) 100%)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:1.94175%;width:80.09709%;height:18.4466%;opacity:1\">\n<div id=\"anim-f34c18d5-944b-4fdb-bed1-4d4ca3717080\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-d7161efd-bf2e-4612-a0b3-9dab4f433f8c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6060606060606061% 0.6060606060606061% 0.6060606060606061% 0.6060606060606061% \/ 1.7543859649122806% 1.7543859649122806% 1.7543859649122806% 1.7543859649122806%\" id=\"el-ac3d2033-e30c-4985-a14f-73d9cb09da37\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.455% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">The following is a collection of integration formulas that are often used to solve integration problems.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:calc(4.85437% - 5px);top:calc(26.3754% - 5px);width:calc(89.32039% + 10px);height:calc(66.66667% + 10px);opacity:1\">\n<div style=\"top:0;left:0;right:0;bottom:0;width:100%;height:100%;position:absolute;border-width:5px 5px 5px 5px;border-color:rgba(255,255,255,1);border-style:solid;border-radius:5.434782608695652% 5.434782608695652% 5.434782608695652% 5.434782608695652% \/ 4.854368932038835% 4.854368932038835% 4.854368932038835% 4.854368932038835%;pointer-events:initial;display:block;z-index:0\" class=\"mask\" id=\"el-9a86a3a5-60cb-426f-97c9-768ccbad8070\">\n<div style=\"position:absolute;width:124.23642%;height:197.27725%;left:-10.90598%;top:-27.65228%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-4-1.png\" alt=\"Integration-formulas-4-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-4-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-4-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-4-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-4-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 40vh, 89vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"f594dfaa-11da-4828-bca2-1b859367fc10\" auto-advance-after=\"9s\"><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#f9fbfb\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-b38d266e-3931-446d-8ef9-5b20c6ac536f\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58.jpg\" alt=\"58\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:calc(4.85437% - 5px);top:calc(8.73786% - 5px);width:calc(90.53398% + 10px);height:calc(84.14239% + 10px);opacity:1\">\n<div style=\"top:0;left:0;right:0;bottom:0;width:100%;height:100%;position:absolute;border-width:5px 5px 5px 5px;border-color:rgba(255,255,255,1);border-style:solid;border-radius:5.361930294906166% 5.361930294906166% 5.361930294906166% 5.361930294906166% \/ 3.8461538461538463% 3.8461538461538463% 3.8461538461538463% 3.8461538461538463%;pointer-events:initial;display:block;z-index:0\" class=\"mask\" id=\"el-eed5a5e1-a667-418f-81cf-cf2202bff13d\">\n<div style=\"position:absolute;width:100%;height:127.52137%;left:0%;top:-11.19367%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-5-1.png\" alt=\"Integration-formulas-5-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-5-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-5-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-5-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-formulas-5-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 41vh, 91vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"b23efef2-26d6-41b1-9148-63ed8991b99e\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-b8bf1159-a441-4961-b3ba-171b17b0eb44\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-0c9e2118-be0c-414d-bdc9-a21d3b822e39\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#fbfbf9\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-efc89fff-4d9f-48c1-80e3-e09e71175630\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg\" alt=\"44\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:10.19417%;top:14.07767%;width:78.15534%;height:5.01618%;opacity:1\">\n<div id=\"anim-b8bf1159-a441-4961-b3ba-171b17b0eb44\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-0c9e2118-be0c-414d-bdc9-a21d3b822e39\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6211180124223602% 0.6211180124223602% 0.6211180124223602% 0.6211180124223602% \/ 6.451612903225806% 6.451612903225806% 6.451612903225806% 6.451612903225806%\" id=\"el-6d9e0e75-77e9-4a3d-bc51-72d806246850\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.5551242236024849% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.404531em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Example :<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:calc(4.24757% - 5px);top:calc(27.99353% - 5px);width:calc(91.50485% + 10px);height:calc(52.10356% + 10px);opacity:1\">\n<div style=\"top:0;left:0;right:0;bottom:0;width:100%;height:100%;position:absolute;border-width:5px 5px 5px 5px;border-color:rgba(255,255,255,1);border-style:solid;border-radius:5.305039787798409% 5.305039787798409% 5.305039787798409% 5.305039787798409% \/ 6.211180124223603% 6.211180124223603% 6.211180124223603% 6.211180124223603%;pointer-events:initial;display:block;z-index:0\" class=\"mask\" id=\"el-0f0ea570-a122-4ae9-add6-a9ba32acb79e\">\n<div style=\"position:absolute;width:118.49249%;height:246.63447%;left:-8.09093%;top:-37.45572%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-Formulas-6-1.png\" alt=\"Integration-Formulas-6-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-Formulas-6-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-Formulas-6-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-Formulas-6-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Integration-Formulas-6-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 41vh, 92vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Integration formula is the inverse of differentiation and it is used to calculate integrals.<\/p>\n","protected":false},"author":1,"featured_media":0,"template":"","meta":{"web_stories_publisher_logo":224645,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[2144,2352],"web_story_tag":[],"class_list":["post-197281","web-story","type-web-story","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Integration Formulas List With Examples | CBSE Class 12 Maths Chapter 7<\/title>\n<meta name=\"description\" content=\"Integration Formulas Class 12: Check out List of basic Integral Formulas \u00b7 \u222b 1 dx = x + C, \u222b a dx = ax+ C, \u222b xn dx = ((xn+1)\/(n+1))+C ; n\u22601, \u222b sin x dx = \u2013 cos x + C, \u222b cos x dx = sin x + C and more on aakash.ac.in\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-integration-formula-explained-with-examples-cbse-class-12-maths\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Integration Formulas List With Examples | CBSE Class 12 Maths Chapter 7\" \/>\n<meta property=\"og:description\" content=\"Integration Formulas Class 12: Check out List of basic Integral Formulas \u00b7 \u222b 1 dx = x + C, \u222b a dx = ax+ C, \u222b xn dx = ((xn+1)\/(n+1))+C ; n\u22601, \u222b sin x dx = \u2013 cos x + C, \u222b cos x dx = sin x + C and more on aakash.ac.in\" \/>\n<meta property=\"og:url\" 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aakash.ac.in","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-integration-formula-explained-with-examples-cbse-class-12-maths\/","og_locale":"en_US","og_type":"article","og_title":"Integration Formulas List With Examples | CBSE Class 12 Maths Chapter 7","og_description":"Integration Formulas Class 12: Check out List of basic Integral Formulas \u00b7 \u222b 1 dx = x + C, \u222b a dx = ax+ C, \u222b xn dx = ((xn+1)\/(n+1))+C ; n\u22601, \u222b sin x dx = \u2013 cos x + C, \u222b cos x dx = sin x + C and more on aakash.ac.in","og_url":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-integration-formula-explained-with-examples-cbse-class-12-maths\/","og_site_name":"Aakash 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