{"id":2013,"date":"2021-12-23T16:00:51","date_gmt":"2021-12-23T10:30:51","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2013"},"modified":"2025-02-28T16:01:56","modified_gmt":"2025-02-28T10:31:56","slug":"ncert-solutions-for-class-12-maths-chapter-7-integrals-ex-7-2-exercise-7-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2"},"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\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#NCERT_Solutions_for_Class_12_Maths_Chapter_7_-_Exercise_72\" title=\"NCERT Solutions for Class 12 Maths Chapter 7 \u2013 Exercise 7.2\">NCERT Solutions for Class 12 Maths Chapter 7 \u2013 Exercise 7.2<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#FAQ\" title=\"FAQ\">FAQ<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">The NCERT exercise 7.2 class 12 solutions are incredibly beneficial to students preparing for their class 12 exams. This paper contains solutions to chapter integration, which is part of chapter exercise 7.2 in <span style=\"color: #0000ff;\"><strong><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\" target=\"_blank\" rel=\"noopener\">class 12 Maths<\/a><\/strong><\/span>. Here you&#8217;ll find detailed answers to the chapter&#8217;s questions. An integral is a mathematical notion that assigns values to functions in order to explain the area, volume, displacement, and all other ideas that come from combining infinitesimal data. These solutions will assist you in learning all of these concepts and putting them into practice.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\">\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? Are you preparing for Exams?<\/span>\n\t\t\t<span class=\"subtitle\">Study without Internet (Offline)<\/span>\n\t\t\t\n\t\t\t<button class=\"download-pdf-btn\" type=\"submit\"><img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/themes\/blog\/assets\/download-icon.svg\" alt=\"Download PDF icon\" width=\"18px\" height=\"18px\">Download PDF<\/button>\n\t\t<\/div>\n\t\t<div class=\"custom-model-main pdf-download-modal\">\n\t\t\t<div class=\"custom-model-inner\">\n\t\t\t\t<div class=\"close-modal-btn close-pdf-btn\">\u00d7<\/div>\n\t\t\t\t<div class=\"custom-model-wrap\">\n\t\t\t\t\t<div class=\"pop-up-content-wrap\">\n\t\t\t\t\t<div role=\"form\" class=\"wpcf7\" id=\"wpcf7-f314520-o1\" lang=\"en-US\" dir=\"ltr\">\n<div class=\"screen-reader-response\"><p role=\"status\" aria-live=\"polite\" aria-atomic=\"true\"><\/p> <ul><\/ul><\/div>\n<form action=\"\/surge\/wp-json\/wp\/v2\/posts\/2013#wpcf7-f314520-o1\" method=\"post\" class=\"wpcf7-form init\" novalidate=\"novalidate\" data-status=\"init\">\n<div style=\"display: none;\">\n<input type=\"hidden\" name=\"_wpcf7\" value=\"314520\" \/>\n<input type=\"hidden\" name=\"_wpcf7_version\" value=\"5.5.6\" \/>\n<input type=\"hidden\" name=\"_wpcf7_locale\" value=\"en_US\" \/>\n<input type=\"hidden\" name=\"_wpcf7_unit_tag\" value=\"wpcf7-f314520-o1\" \/>\n<input type=\"hidden\" name=\"_wpcf7_container_post\" value=\"0\" \/>\n<input type=\"hidden\" name=\"_wpcf7_posted_data_hash\" value=\"\" \/>\n<input type=\"hidden\" name=\"_wpcf7_recaptcha_response\" value=\"\" \/>\n<\/div>\n<div class=\"inline-form\">\n<p class=\"title\">Download PDF for Free.<br \/>\nStudy without Internet (Offline)<\/p>\n<p><span class=\"wpcf7-form-control-wrap your-first-name\"><input type=\"text\" name=\"your-first-name\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-validates-as-required\" id=\"user_name\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"First Name\" \/><\/span><\/p>\n<p><span class=\"wpcf7-form-control-wrap your-last-name\"><input type=\"text\" name=\"your-last-name\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-validates-as-required\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"Last Name\" \/><\/span><\/p>\n<p>  <label>Grade<\/label><br \/>\n  <span class=\"wpcf7-form-control-wrap your-grade\"><select name=\"your-grade\" class=\"wpcf7-form-control wpcf7-select wpcf7-validates-as-required grades-select\" aria-required=\"true\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"Class 1\">Class 1<\/option><option value=\"Class 2\">Class 2<\/option><option value=\"Class 3\">Class 3<\/option><option value=\"Class 4\">Class 4<\/option><option value=\"Class 5\">Class 5<\/option><option value=\"Class 6\">Class 6<\/option><option value=\"Class 7\">Class 7<\/option><option value=\"Class 8\">Class 8<\/option><option value=\"Class 9\">Class 9<\/option><option value=\"Class 10\">Class 10<\/option><option value=\"Class 11\">Class 11<\/option><option value=\"Class 12\">Class 12<\/option><\/select><\/span><\/p>\n<p>  <label>Target Exam<\/label><br \/>\n  <span class=\"wpcf7-form-control-wrap target-exam\"><select name=\"target-exam\" class=\"wpcf7-form-control wpcf7-select wpcf7-validates-as-required target-exam-select\" aria-required=\"true\" aria-invalid=\"false\"><option value=\"JEE\">JEE<\/option><option value=\"NEET\">NEET<\/option><option value=\"CBSE\">CBSE<\/option><\/select><\/span><\/p>\n<p style=\"display: flex;align-items: center;gap: 0.2rem;\">\n+91 <span class=\"wpcf7-form-control-wrap your-phone\"><input type=\"tel\" name=\"your-phone\" value=\"\" size=\"40\" maxlength=\"10\" minlength=\"10\" class=\"wpcf7-form-control wpcf7-text wpcf7-tel wpcf7-validates-as-required wpcf7-validates-as-tel\" id=\"otp_phone\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"Phone number\" \/><\/span>\n<\/p>\n<div id=\"otp_message\" class=\"otp_message\"><\/div>\n<p><label>Preferred time slot for the call<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap timeslot\"><select name=\"timeslot\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"9 am\">9 am<\/option><option value=\"10 am\">10 am<\/option><option value=\"11 am\">11 am<\/option><option value=\"12 pm\">12 pm<\/option><option value=\"1 pm\">1 pm<\/option><option value=\"2 pm\">2 pm<\/option><option value=\"3 pm\">3 pm<\/option><option value=\"4 pm\">4 pm<\/option><option value=\"5 pm\">5 pm<\/option><option value=\"6 pm\">6 pm<\/option><option value=\"7 pm\">7 pm<\/option><option value=\"8pm\">8pm<\/option><option value=\"9 pm\">9 pm<\/option><option value=\"10pm\">10pm<\/option><\/select><\/span><\/p>\n<p><label>Please indicate your interest<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap intent-checkbox\"><span class=\"wpcf7-form-control wpcf7-checkbox\"><span class=\"wpcf7-list-item first\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Live Classes\" \/><span class=\"wpcf7-list-item-label\">Live Classes<\/span><\/span><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Books\" \/><span class=\"wpcf7-list-item-label\">Books<\/span><\/span><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Test Series\" \/><span class=\"wpcf7-list-item-label\">Test Series<\/span><\/span><span class=\"wpcf7-list-item last\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Self Learning\" \/><span class=\"wpcf7-list-item-label\">Self Learning<\/span><\/span><\/span><\/span><\/p>\n<p><label>Language<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap language\"><select name=\"language\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"English\">English<\/option><option value=\"Hindi\">Hindi<\/option><option value=\"Marathi\">Marathi<\/option><option value=\"Tamil\">Tamil<\/option><option value=\"Telugu\">Telugu<\/option><option value=\"Malayalam\">Malayalam<\/option><\/select><\/span><\/p>\n<p><label>Are you a Sri Chaitanya student?<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap sri-chaitanya-student\"><select name=\"sri-chaitanya-student\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"No\">No<\/option><option value=\"Yes\">Yes<\/option><\/select><\/span><\/p>\n<style>\n.intent-checkbox .wpcf7-checkbox{\n    display: flex;\n    flex-wrap: wrap;\n}\n.intent-checkbox .wpcf7-checkbox .wpcf7-list-item {\n    width: 50%;\n    margin: 0!important;\n    padding: 0.1rem;\n}\n<\/style>\n<p class=\"verify_otp_input\">Verify OTP Code (required)<br \/><span class=\"wpcf7-form-control-wrap phone_verify\"><input type=\"number\" name=\"phone_verify\" value=\"\" class=\"wpcf7-form-control wpcf7-number wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/2013\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-7.2.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-7.2.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Exercise 7.2<br\/><\/a><\/span><\/p>\n<h2 aria-level=\"2\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_7_-_Exercise_72\"><\/span>NCERT Solutions for Class 12 Maths Chapter 7 \u2013 Exercise 7.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">One of the most important operations in calculus is integration, and the other is differentiation. One of the additive constants used to distinguish between characters is the integration operation. It is the calculus fundamental theorem that connects differentiation with definite integral.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">In the late 17th century, the famous Isaac Newton and another prominent scholar Gottfried Wilhelm Leibniz separately devised the concepts of integration, thinking of integral as an endless sum of rectangles of infinitesimal width. Later, Bernhard Riemann developed a mathematical definition of integrals that is based on a limiting approach that approximates the entire area of a curved region by splitting it into thin vertical slabs separately.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\" target=\"_blank\" rel=\"noopener\"><strong>Class 12 Maths NCERT solutions<\/strong><\/a><\/span> chapter 7 exercise 7.2 will teach you that the beginning of the 19th century was when more sophisticated conceptions of integrals began to appear. When, where, the type of function, and the domain across which the integration is done were all generalized during this time. A line integral is a function of variables that are covered (2 or more in number). A curve connects the two endpoints and takes the place of the integration interval. A piece of surface replaces the curve when the surface integral is applied in a 3D space.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Formalization<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Despite the fact that Newton and Leibniz devised a methodical approach to integration, it had some flaws in terms of rigor. Bishop Berkeley was hostile to Newton&#8217;s notion, which he dubbed &#8220;ghosts of departed quantities.&#8221; Calculus was more widely recognized when it came to the development of limits. Riemann was the first to formalize integration with limits in 1854.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">On a bounded interval, all bounded piecewise continuous functions are Riemann-integrable, but more generic functions\u2014particularly in the context of Fourier analysis\u2014were also considered, to which Riemann&#8217;s definition does not apply. Lebesgue devised a new definition of integral that differed from previous definitions and incorporated the concept of measure theory, which covered real or subfield analysis.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<h4><span class=\"ez-toc-section\" id=\"FAQ\"><\/span><span style=\"font-size: 18pt;\"><b>FAQ<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><b><span data-contrast=\"auto\"><span style=\"color: #0000ff;\">Question. What are the three most popular and helpful integration methods in calculus<\/span>?<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276}\"> <span style=\"color: #ff0000;\"><strong>Answer.<\/strong> <\/span><\/span><span data-contrast=\"auto\">The following are the three most common ways of integration:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"3\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">Method of substitution<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:1440,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"3\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">The Method of Partial Fractions<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:1440,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"3\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"auto\">Parts-based integration<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:1440,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">Problems of integration of various forms are covered in class 12 maths chapter 7 ex 7.2. Each approach has its own set of principles that must be properly understood before the integration can be completed.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span style=\"color: #0000ff;\"><b>Question. What are the various uses for definite integrals?<\/b><\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #ff0000;\"><strong>Answer.<\/strong><\/span> In arithmetic, science, and economics, integration is used to determine the worth of a variety of objects. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The following are some of the most important applications of definite integrals:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">The circumference of a curve-bound region<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">The volume of a solid whose cross-section has been determined.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"auto\">Arc length is the measurement of how long an arc is.<\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">Fluids&#8217; pressure<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">Integration and electric circuits<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"auto\">Moment of inertia is a term that refers to the inertia<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><span style=\"color: #0000ff;\"><b>Question. Is Maths in Class 12 difficult?<\/b><\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #ff0000;\"><strong>Answer.<\/strong><\/span> Many students despise math and find Class 12 math to be extremely difficult. This, however, may not be the case. Everything is up to you and your plan. You will not be able to do well if you have a negative outlook. You must practice Class 12 Maths on a daily basis, and Infinity Learn&#8217;s NCERT Solutions Class 12 Maths is the ideal friend that can make things easier for you.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The NCERT exercise 7.2 class 12 solutions are incredibly beneficial to students preparing for their class 12 exams. This paper [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Class 12 Maths Chapter 7 Integrals Exercise 7.2","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2","_yoast_wpseo_metadesc":"Get NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2, Get help of our tutors and understand the concepts.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/"},"categories":[13,19,31,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2<\/title>\n<meta name=\"description\" content=\"Get NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2, Get help of our tutors and understand the concepts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2\" \/>\n<meta property=\"og:description\" content=\"Get NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2, Get help of our tutors and understand the concepts.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-12-23T10:30:51+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-02-28T10:31:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasad Gupta\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2","description":"Get NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2, Get help of our tutors and understand the concepts.","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:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2","og_description":"Get NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2, Get help of our tutors and understand the concepts.","og_url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2021-12-23T10:30:51+00:00","article_modified_time":"2025-02-28T10:31:56+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"Prasad Gupta","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/","name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2021-12-23T10:30:51+00:00","dateModified":"2025-02-28T10:31:56+00:00","description":"Get NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2, Get help of our tutors and understand the concepts.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.2) Exercise 7.2","datePublished":"2021-12-23T10:30:51+00:00","dateModified":"2025-02-28T10:31:56+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7\/integrals\/exercise-7-2\/#webpage"},"wordCount":655,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["Maths","NCERT Solutions","NCERT Solutions For Class 12 Mathematics","Study Materials"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05","name":"Prasad Gupta","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","caption":"Prasad Gupta"},"url":"https:\/\/infinitylearn.com\/surge\/author\/prasad\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/2013"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=2013"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/2013\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=2013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=2013"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=2013"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=2013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}