{"id":2234,"date":"2021-12-24T14:53:29","date_gmt":"2021-12-24T09:23:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2234"},"modified":"2024-07-03T11:12:00","modified_gmt":"2024-07-03T05:42:00","slug":"ncert-solutions-for-class-12-maths-chapter-8-application-of-integrals-ex-8-2-exercise-8-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.2"},"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-8-application-of-integrals-exercise-8-2\/#NCERT_Solutions_for_Class_12_Maths_Chapter_8_Application_of_Integrals_Exercise_82_-_CBSE_Free_PDF_Download\" title=\"NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.2 \u2013 CBSE Free PDF Download\">NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.2 \u2013 CBSE Free PDF Download<\/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-8-application-of-integrals-exercise-8-2\/#NCERT_Solutions_Class_12_Maths_Chapter_8_Exercise_82_Tips\" title=\"NCERT Solutions Class 12 Maths Chapter 8 Exercise 8.2 Tips\">NCERT Solutions Class 12 Maths Chapter 8 Exercise 8.2 Tips<\/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-8-application-of-integrals-exercise-8-2\/#Frequently_Asked_Questions_FAQs\" title=\"Frequently Asked Questions (FAQs)\">Frequently Asked Questions (FAQs)<\/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-8-application-of-integrals-exercise-8-2\/#What_is_the_difficulty_level_of_the_problems_in_NCERT_solutions_for_Class_12_Maths_Chapter_8_Exercise_82\" title=\"What is the difficulty level of the problems in NCERT solutions for Class 12 Maths Chapter 8, Exercise 8.2?\">What is the difficulty level of the problems in NCERT solutions for Class 12 Maths Chapter 8, Exercise 8.2?<\/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-8-application-of-integrals-exercise-8-2\/#How_can_students_effectively_determine_the_limits_of_integration_for_given_curves_in_Exercise_82\" title=\"How can students effectively determine the limits of integration for given curves in Exercise 8.2?\">How can students effectively determine the limits of integration for given curves in Exercise 8.2?<\/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-8-application-of-integrals-exercise-8-2\/#What_should_students_do_if_they_encounter_difficulties_while_solving_Exercise_82_in_Chapter_8\" title=\"What should students do if they encounter difficulties while solving Exercise 8.2 in Chapter 8?\">What should students do if they encounter difficulties while solving Exercise 8.2 in Chapter 8?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">NCERT Solutions for Class 12 Maths Chapter 8, Application of Integrals, provides detailed solutions for all questions in Exercise 8.2. The solutions include diagrams and easy-to-understand methods. Download the NCERT Maths Solutions for Class 12 and practice to excel in the board exams.<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_8_Application_of_Integrals_Exercise_82_-_CBSE_Free_PDF_Download\"><\/span>NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.2 \u2013 CBSE Free PDF Download<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download the free PDF of NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2, prepared by expert Mathematics teachers at Infinity Learn, following CBSE (NCERT) guidelines. Use these solutions for Chapter 8, Application of Integrals, Exercise 8.2 to thoroughly revise the syllabus and score higher marks 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\/2234#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\/2234\" 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-8.2.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-8.2.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 8.2<br\/><\/a>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Chapter_8_Exercise_82_Tips\"><\/span>NCERT Solutions Class 12 Maths Chapter 8 Exercise 8.2 Tips<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals\/\"><strong>NCERT solutions for Class 12 Maths Chapter 8<\/strong><\/a>, Exercise 8.2 on the application of integrals, includes 7 problems ranging from intermediate to complex levels. To determine the limits of integration and when to switch formulas for given curves, it&#8217;s essential to draw graphs and shade the required regions. This topic is highly scoring for students with a solid understanding of the concepts.<\/p>\n<p>The questions in <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\"><strong>NCERT solutions for Class 12 Maths<\/strong><\/a> Chapter 8 are arranged in various formats, allowing students to review the types of problems that might appear in exams. If students face difficulties with this exercise, they should revisit the topics of integration and curves or seek help from their teachers. It is important to address queries promptly to avoid gaps in learning and ensure a strong mathematical foundation. Download <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>Infinity Learn NCERT Solutions<\/strong> <\/a>PDF for free and start learning.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_FAQs\"><\/span>Frequently Asked Questions (FAQs)<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=\"What_is_the_difficulty_level_of_the_problems_in_NCERT_solutions_for_Class_12_Maths_Chapter_8_Exercise_82\"><\/span>What is the difficulty level of the problems in NCERT solutions for Class 12 Maths Chapter 8, Exercise 8.2?<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 problems in this exercise range from intermediate to complex levels, requiring a solid understanding of integrals and curves.\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=\"How_can_students_effectively_determine_the_limits_of_integration_for_given_curves_in_Exercise_82\"><\/span>How can students effectively determine the limits of integration for given curves in Exercise 8.2?<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\tStudents should draw graphs and shade the required regions to accurately identify the limits of integration and understand when to switch formulas.\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_should_students_do_if_they_encounter_difficulties_while_solving_Exercise_82_in_Chapter_8\"><\/span>What should students do if they encounter difficulties while solving Exercise 8.2 in Chapter 8?<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\tIf students face difficulties, they should revisit the topics of integration and curves or seek help from their teachers to ensure a strong understanding and avoid gaps in learning.\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\": \"What is the difficulty level of the problems in NCERT solutions for Class 12 Maths Chapter 8, Exercise 8.2?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The problems in this exercise range from intermediate to complex levels, requiring a solid understanding of integrals and curves.\"\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\": \"How can students effectively determine the limits of integration for given curves in Exercise 8.2?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Students should draw graphs and shade the required regions to accurately identify the limits of integration and understand when to switch formulas.\"\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 should students do if they encounter difficulties while solving Exercise 8.2 in Chapter 8?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"If students face difficulties, they should revisit the topics of integration and curves or seek help from their teachers to ensure a strong understanding and avoid gaps in learning.\"\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>NCERT Solutions for Class 12 Maths Chapter 8, Application of Integrals, provides detailed solutions for all questions in Exercise 8.2. [&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":"NCERT Solutions for Class 12 Maths","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Ch-8 Exercise 8.2","_yoast_wpseo_metadesc":"Class 12 Maths NCERT Solutions Chapter 8 Exercise 8.2 on the Application of Integrals - Download the free PDF of Class 12 Maths NCERT Solutions for Chapter 8 Exercise 8.2 and practice these solutions to enhance your understanding of the concepts, aiding CBSE school students in their studies.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/"},"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 Ch-8 Exercise 8.2<\/title>\n<meta name=\"description\" content=\"Class 12 Maths NCERT Solutions Chapter 8 Exercise 8.2 on the Application of Integrals - Download the free PDF of Class 12 Maths NCERT Solutions for Chapter 8 Exercise 8.2 and practice these solutions to enhance your understanding of the concepts, aiding CBSE school students in their studies.\" \/>\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-8-application-of-integrals-exercise-8-2\/\" \/>\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 Ch-8 Exercise 8.2\" \/>\n<meta property=\"og:description\" content=\"Class 12 Maths NCERT Solutions Chapter 8 Exercise 8.2 on the Application of Integrals - Download the free PDF of Class 12 Maths NCERT Solutions for Chapter 8 Exercise 8.2 and practice these solutions to enhance your understanding of the concepts, aiding CBSE school students in their studies.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/\" \/>\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=\"2021-12-24T09:23:29+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-07-03T05:42:00+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 Ch-8 Exercise 8.2","description":"Class 12 Maths NCERT Solutions Chapter 8 Exercise 8.2 on the Application of Integrals - Download the free PDF of Class 12 Maths NCERT Solutions for Chapter 8 Exercise 8.2 and practice these solutions to enhance your understanding of the concepts, aiding CBSE school students in their studies.","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-8-application-of-integrals-exercise-8-2\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Ch-8 Exercise 8.2","og_description":"Class 12 Maths NCERT Solutions Chapter 8 Exercise 8.2 on the Application of Integrals - Download the free PDF of Class 12 Maths NCERT Solutions for Chapter 8 Exercise 8.2 and practice these solutions to enhance your understanding of the concepts, aiding CBSE school students in their studies.","og_url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2021-12-24T09:23:29+00:00","article_modified_time":"2024-07-03T05:42:00+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-8-application-of-integrals-exercise-8-2\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/","name":"NCERT Solutions for Class 12 Maths Ch-8 Exercise 8.2","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2021-12-24T09:23:29+00:00","dateModified":"2024-07-03T05:42:00+00:00","description":"Class 12 Maths NCERT Solutions Chapter 8 Exercise 8.2 on the Application of Integrals - Download the free PDF of Class 12 Maths NCERT Solutions for Chapter 8 Exercise 8.2 and practice these solutions to enhance your understanding of the concepts, aiding CBSE school students in their studies.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/#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 8 Application of Integrals Exercise 8.2"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.2","datePublished":"2021-12-24T09:23:29+00:00","dateModified":"2024-07-03T05:42:00+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-2\/#webpage"},"wordCount":404,"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\/2234"}],"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=2234"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/2234\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=2234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=2234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=2234"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=2234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}