{"id":2017,"date":"2021-12-23T16:02:57","date_gmt":"2021-12-23T10:32:57","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2017"},"modified":"2025-06-03T17:35:37","modified_gmt":"2025-06-03T12:05:37","slug":"ncert-solutions-for-class-12-maths-chapter-7-integrals-ex-7-3-exercise-7-3","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.3) Exercise 7.3"},"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-7-3\/#Class_12_Maths_NCERT_Solutions_For_Chapter_7_Exercise_73\" title=\"Class 12 Maths NCERT Solutions For Chapter 7 Exercise 7.3\">Class 12 Maths NCERT Solutions For Chapter 7 Exercise 7.3<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><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-7-3\/#Class_12_Maths_Chapter_7_Exercise_73_NCERT_Solutions_Benefits\" title=\"Class 12 Maths Chapter 7 Exercise 7.3 NCERT Solutions Benefits\">Class 12 Maths Chapter 7 Exercise 7.3 NCERT Solutions Benefits<\/a><\/li><\/ul><\/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\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#FAQs_on\" title=\"FAQs on\">FAQs on<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#In_Class_12_Maths_Chapter_7_Exercise_73_what_is_the_concept_of_Integral_Calculus\" title=\"In Class 12 Maths Chapter 7 Exercise 7.3, what is the concept of Integral Calculus?\">In Class 12 Maths Chapter 7 Exercise 7.3, what is the concept of Integral Calculus?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#Is_it_beneficial_to_study_from_the_NCERT_Solutions_for_Exercise_73_in_Class_12\" title=\"Is it beneficial to study from the NCERT Solutions for Exercise 7.3 in Class 12?\">Is it beneficial to study from the NCERT Solutions for Exercise 7.3 in Class 12?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#What_are_the_most_essential_concepts_addressed_in_Class_12_Maths_Chapter_7_Exercise_73\" title=\"What are the most essential concepts addressed in Class 12 Maths Chapter 7 Exercise 7.3?\">What are the most essential concepts addressed in Class 12 Maths Chapter 7 Exercise 7.3?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Our team of experts is committed to producing top-notch study materials tailored for Chapter 7.3 on Integrals in 12th-grade Mathematics. Infinity Learn&#8217;s <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\"><strong>NCERT Solutions for Class 12 Maths<\/strong><\/a> Chapter 7, Exercise 7.3, is meticulously designed to comprehensively cover different aspects of Integrals, enhancing students&#8217; learning experiences to the fullest. Over the years, Chapter 7, Exercise 7.3 in 12th-grade Mathematics has proven to be an essential topic, and practicing from this section offers a significant advantage due to its straightforward mathematical solutions. Moreover, this particular exercise holds considerable weight in both sections of the question paper, making it even more critical. Therefore, our printable PDF of NCERT Solutions for Class 12 Maths Chapter 7, Exercise 7.3, equips you with the additional support needed to excel in your exams.<\/p>\n\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\/2017#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\/2017\" 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-7.3.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-7.3.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 7.3<br\/><\/a>\n<h2><span class=\"ez-toc-section\" id=\"Class_12_Maths_NCERT_Solutions_For_Chapter_7_Exercise_73\"><\/span>Class 12 Maths NCERT Solutions For Chapter 7 Exercise 7.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The application of numbers representing various functions, strategically placed to assist us in uncovering and explaining the outcomes related to various phenomena such as area, displacement, volume, and other infinitesimal data-related concepts, is the primary focus of Chapter 7.3 Integrals in Class 12 Mathematics. Integration is a fundamental part of calculus that can also be employed in inverse operations and differentiation.<\/p>\n<p>These recommended functions are known as antiderivatives when a particular solution can be derived from a given function &#8216;f&#8217; within a specific range of values. This means that the derivative &#8216;f&#8217; exists at every suggested point within the interval. You can find detailed explanations of this concept in Class 12 Mathematicsfor Exercise 7.3.<\/p>\n<p>Infinity Learn offers valuable Miscellaneous Exercise solutions for Class 12 Mathematics, particularly concerning the topic of &#8216;rate of change of quantities.&#8217; Additionally, you can find individual solutions for other chapters in Class 12 Mathematics.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Class_12_Maths_Chapter_7_Exercise_73_NCERT_Solutions_Benefits\"><\/span>Class 12 Maths Chapter 7 Exercise 7.3 NCERT Solutions Benefits<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>The following are some of the advantages of using NCERT solutions for Exercise 7.3 in-class 12 maths:<\/strong><\/p>\n<ul>\n<li>All exercises in the textbook include Infinity Learn NCERT math solutions, designed to reduce the stress on students.<\/li>\n<li>These solutions can be easily downloaded and printed, making them convenient for all students.<\/li>\n<li>Expert math teachers have authored these solutions to ensure accuracy and reliability.<\/li>\n<li>Infinity Learn provides these solutions free of charge, making them accessible to all.<\/li>\n<\/ul>\n<p><strong>Also Check:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-1\/\" target=\"_blank\" rel=\"noopener\"><strong>Exercise 7.1 Solutions<\/strong><\/a><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-2\" target=\"_blank\" rel=\"noopener\">Exercise 7.2 Solutions <\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-4\" target=\"_blank\" rel=\"noopener\">Exercise 7.4 Solutions <\/a><\/strong><\/li>\n<li><strong>Exercise 7.5 Solutions<\/strong><\/li>\n<li><strong>Exercise 7.6 Solutions<\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-7\" target=\"_blank\" rel=\"noopener\">Exercise 7.7 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-8\" target=\"_blank\" rel=\"noopener\">Exercise 7.8 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-9\" target=\"_blank\" rel=\"noopener\">Exercise 7.9 Solutions <\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-10\" target=\"_blank\" rel=\"noopener\">Exercise 7.10 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-11\" target=\"_blank\" rel=\"noopener\">Exercise 7.11 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-miscellaneous\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise for Chapter 7 Solutions<\/a><\/strong><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on\"><\/span>FAQs on<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"In_Class_12_Maths_Chapter_7_Exercise_73_what_is_the_concept_of_Integral_Calculus\"><\/span>In Class 12 Maths Chapter 7 Exercise 7.3, what is the concept of Integral Calculus?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe rationale behind the development of integral calculus addresses a variety of math-related issues. Users that find it tough to deal with the various solutions of the given kind would benefit from this concept:  When given a derivative, they must find a function.  Finding regions when they are bordered by graphs and bound by specific requirements might be difficult.  These two problems are the foundations for developing Integral Calculus by offering forms that allow integrals, such as indefinite and definite integrals. In Exercise 7.3 Class 12 Maths, this section is thoroughly addressed and explained. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Is_it_beneficial_to_study_from_the_NCERT_Solutions_for_Exercise_73_in_Class_12\"><\/span>Is it beneficial to study from the NCERT Solutions for Exercise 7.3 in Class 12?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tStudying from the NCERT answers for Exercise 7.3 Maths Class 12 benefits students in a variety of ways. To begin, the solutions are entirely focused on addressing the most difficult and significant questions of integrals from their roots in order to facilitate Ex 7.3 Class 12 Maths learning. The solutions were shown by a group of committed professors and are aimed at assisting students in grasping the many topics covered in the intervals part. The Ex 7.3 Class 12 Maths Solutions supplied are mostly designed for students taking the current year's CBSE curriculum Class 12 Board exams. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_most_essential_concepts_addressed_in_Class_12_Maths_Chapter_7_Exercise_73\"><\/span>What are the most essential concepts addressed in Class 12 Maths Chapter 7 Exercise 7.3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIntegrals is the title of Chapter 7 of NCERT Class 12 Maths. This is an important chapter in the Class 12 Maths syllabus, with a substantial weighting in terms of marks. While the chapter covers a variety of key topics, Exercise 7.3, which comprises Integration by Substitution, Integration using Partial, and Fractions Integration by Parts is one of the most significant that students should study for and practice on a regular basis. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"In Class 12 Maths Chapter 7 Exercise 7.3, what is the concept of Integral Calculus?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The rationale behind the development of integral calculus addresses a variety of math-related issues. Users that find it tough to deal with the various solutions of the given kind would benefit from this concept:  When given a derivative, they must find a function.  Finding regions when they are bordered by graphs and bound by specific requirements might be difficult.  These two problems are the foundations for developing Integral Calculus by offering forms that allow integrals, such as indefinite and definite integrals. In Exercise 7.3 Class 12 Maths, this section is thoroughly addressed and explained.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Is it beneficial to study from the NCERT Solutions for Exercise 7.3 in Class 12?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Studying from the NCERT answers for Exercise 7.3 Maths Class 12 benefits students in a variety of ways. To begin, the solutions are entirely focused on addressing the most difficult and significant questions of integrals from their roots in order to facilitate Ex 7.3 Class 12 Maths learning. The solutions were shown by a group of committed professors and are aimed at assisting students in grasping the many topics covered in the intervals part. The Ex 7.3 Class 12 Maths Solutions supplied are mostly designed for students taking the current year's CBSE curriculum Class 12 Board exams.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the most essential concepts addressed in Class 12 Maths Chapter 7 Exercise 7.3?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Integrals is the title of Chapter 7 of NCERT Class 12 Maths. This is an important chapter in the Class 12 Maths syllabus, with a substantial weighting in terms of marks. While the chapter covers a variety of key topics, Exercise 7.3, which comprises Integration by Substitution, Integration using Partial, and Fractions Integration by Parts is one of the most significant that students should study for and practice on a regular basis.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Our team of experts is committed to producing top-notch study materials tailored for Chapter 7.3 on Integrals in 12th-grade Mathematics. [&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":"exercise 7.3 class 12 maths","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.3","_yoast_wpseo_metadesc":"NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals, Exercise 7.3: Detailed, easy-to-understand solutions by teacher.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/"},"categories":[19,31],"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 7.3<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals, Exercise 7.3: Detailed, easy-to-understand solutions by teacher.\" \/>\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-7-3\/\" \/>\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 7.3\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals, Exercise 7.3: Detailed, easy-to-understand solutions by teacher.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/\" \/>\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=\"2021-12-23T10:32:57+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-03T12:05:37+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=\"4 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.3","description":"NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals, Exercise 7.3: Detailed, easy-to-understand solutions by teacher.","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-7-3\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.3","og_description":"NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals, Exercise 7.3: Detailed, easy-to-understand solutions by teacher.","og_url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2021-12-23T10:32:57+00:00","article_modified_time":"2025-06-03T12:05:37+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":"4 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-7-3\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/","name":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.3","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2021-12-23T10:32:57+00:00","dateModified":"2025-06-03T12:05:37+00:00","description":"NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals, Exercise 7.3: Detailed, easy-to-understand solutions by teacher.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#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 7.3) Exercise 7.3"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.3) Exercise 7.3","datePublished":"2021-12-23T10:32:57+00:00","dateModified":"2025-06-03T12:05:37+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-3\/#webpage"},"wordCount":708,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["NCERT Solutions","NCERT Solutions For Class 12 Mathematics"],"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\/2017"}],"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=2017"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/2017\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=2017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=2017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=2017"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=2017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}