{"id":153804,"date":"2022-03-25T22:49:50","date_gmt":"2022-03-25T17:19:50","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/integration-by-substitution-definition-and-examples\/"},"modified":"2022-12-31T17:30:07","modified_gmt":"2022-12-31T12:00:07","slug":"integration-by-substitution-definition-and-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/integration-by-substitution\/","title":{"rendered":"Integration by Substitution \u2013 Definition and Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/integration-by-substitution\/#Integration_by_Substitution_Class_12th\" title=\"Integration by Substitution Class 12th\">Integration by Substitution Class 12th<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/integration-by-substitution\/#What_is_Integration\" title=\"What is Integration?\">What is Integration?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/integration-by-substitution\/#Integration_Examples\" title=\"Integration Examples\">Integration Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/integration-by-substitution\/#What_should_be_used_for_u_in_the_integral\" title=\"What should be used for u in the integral?\">What should be used for u in the integral?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Integration_by_Substitution_Class_12th\"><\/span>Integration by Substitution Class 12th<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Integration by substitution is a technique to integrate a function of the form<\/p>\n<p>This can be done by using the substitution rule to transform the function into a simpler form.<\/p>\n<p>The substitution rule states that:<\/p>\n<p>The substitution rule can be used to transform the function into a simpler form. In this example, the function can be transformed into a linear function.<\/p>\n<p>The substitution rule can be used to transform the function into a simpler form. In this example, the function can be transformed into a quadratic function.<\/p>\n<p>The substitution rule can be used to transform the function into a simpler form. In this example, the function can be transformed into a cubic function.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153803 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/integration-by-substitution-definition-and-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/integration-by-substitution-definition-and-examples.jpg?v=1648228786 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/integration-by-substitution-definition-and-examples-300x212.jpg?v=1648228786 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Integration\"><\/span>What is Integration?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics, integration is the process of finding the area under a curve. Integration is one of the fundamental operations of calculus.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Integration_Examples\"><\/span>Integration Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Integration is the mathematical process of finding the area of a curved region by finding the sum of the areas of its many infinitesimal rectangular regions. Let&#8217;s look at a couple of integration examples to better understand how this works.<\/p>\n<p>Example 1: Find the area of the region bounded by the curves y = x2 and y = x.<\/p>\n<p>We can think of this region as a series of infinitesimal rectangular regions, as shown below.<\/p>\n<p>To find the area of this region, we will need to find the sum of the areas of all of these rectangles. We can do this by using the formula for the sum of a series:<\/p>\n<p>S = \u2211(x i y i )<\/p>\n<p>We can plug in our values for x and y to get:<\/p>\n<p>S = \u2211(x i y i )<\/p>\n<p>S = \u2211(x2)<\/p>\n<p>S = x3<\/p>\n<p>So, the area of the region is x3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_should_be_used_for_u_in_the_integral\"><\/span>What should be used for u in the integral?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The symbol u can be used for any variable in an integral.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Integration by Substitution Class 12th Integration by substitution is a technique to integrate a function of the form This can [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Integration by Substitution","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Integration by Substitution topic of Maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/integration-by-substitution\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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