{"id":2232,"date":"2021-12-24T14:52:56","date_gmt":"2021-12-24T09:22:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2232"},"modified":"2025-05-16T16:23:00","modified_gmt":"2025-05-16T10:53:00","slug":"ncert-solutions-for-class-12-maths-chapter-8-application-of-integrals-ex-8-1-exercise-8-1","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals (Ex 8.1) Exercise 8.1"},"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-3'><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-8-1\/#FAQ\" title=\"FAQ:\">FAQ:<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><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-8-1\/#In_math_Class_12_which_chapters_have_been_removed\" title=\"In math Class 12, which chapters have been removed?\">In math Class 12, which chapters have been removed?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><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-8-1\/#How_will_I_be_able_to_comprehend_the_chapters_in_Class_12_Maths\" title=\"How will I be able to comprehend the chapters in Class 12 Maths?\">How will I be able to comprehend the chapters in Class 12 Maths?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><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-8-1\/#What_is_the_underlying_concept_of_Chapter_8_Application_of_Integrals\" title=\"What is the underlying concept of Chapter 8 Application of Integrals?\">What is the underlying concept of Chapter 8 Application of Integrals?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><strong>NCERT Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.1<\/strong><\/p>\n<p><span data-contrast=\"auto\">All of the questions that must be studied are answered in the NCERT Solutions for Class 12 Maths Chapter 8 Integrals Exercise 8.1. With the appropriate notes, NCERT Maths Class 12 Exercise 8.1 Solutions are straightforward to understand. The Class 12 Maths Chapter 8 Exercise 8.1 Solutions from Infinity Learn are quite useful. Infinity Learn has developed notes that are simple to comprehend for students who desire to excel in their exams. Download the CBSE Class 12 Maths Chapter 8 Integrals PDF for free.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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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\/2232\" 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-8.1.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-8.1.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 8.1<br\/><\/a>\n<p aria-level=\"2\"><span style=\"color: #0000ff;\"><b>NCERT Solutions for Class 12 Maths Chapter 8 Applications of Exercise 8.1 <\/b> <\/span><\/p>\n<p><span data-contrast=\"auto\">When it comes to exam preparation, the NCERT solutions for Miscellaneous Exercise  Class 12 Maths are considered to be the finest alternative for CBSE students. There are a lot of exercises in this chapter. We&#8217;ve included the Miscellaneous Exercise <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\" target=\"_blank\" rel=\"noopener\">Class 12 Maths NCERT solutions<\/a><\/span> in PDF format on this page. You can either download this solution or study it immediately from our website\/app.<\/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\">Infinity learns in-house subject matter specialists addressed the exercise&#8217;s problems\/questions with great care and precision, adhering to all CBSE criteria. Any student in Class 12 who understands all of the concepts from the Maths textbook and is well-versed in all of the problems from the exercises can easily achieve the greatest possible grade on the final exam. Students can easily grasp the pattern of questions that may be asked in the exam from this chapter and also study the marks weightage of the chapter with the assistance of this Class 12 Maths Chapter 8 Exercise 8.1 solutions. So that they can adequately prepare for the final examination.<\/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;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Apart from these <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/\" target=\"_blank\" rel=\"noopener\">NCERT solutions for Class 12<\/a><\/span> Maths Chapter 8 Exercise 8.1, this chapter contains numerous exercises with numerous questions. As previously said, our in-house subject specialists solve\/answer all of these questions. As a result, all of these are guaranteed to be of high quality, and anyone can use them to study for exams. It is critical to grasp all of the topics in the textbooks and solve the questions from the exercises supplied next to them in order to achieve the highest possible grade in the class. Don&#8217;t put it off any longer. For better exam preparation, get the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #3366ff;\">NCERT solutions<\/span><\/a> for Class 12 Maths Chapter 8 Exercise 8.1 from the Infinity Learn website today. If you have the Infinity Learn app installed on your phone, you may also download it from there. The nice thing about these solutions is that they can be used both online and offline.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"FAQ\"><\/span><span style=\"color: #0000ff;\"><b>FAQ:<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"In_math_Class_12_which_chapters_have_been_removed\"><\/span>In math Class 12, which chapters have been removed?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe CBSE syllabus for Class 12 Maths has been lowered by 30%, according to the new CBSE syllabus. Full chapters have not been eliminated from the CBSE Class 12 Maths syllabus, although portions of each unit have been removed. Download the NCERT Solutions Maths Chapter 8 PDF, which is only accessible on Infinity Learn, to acquire the whole NCERT Solutions Maths Chapter 8 based on the most recent curriculum. For a better understanding, extra important questions are also answered\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<h5><span class=\"ez-toc-section\" id=\"How_will_I_be_able_to_comprehend_the_chapters_in_Class_12_Maths\"><\/span>How will I be able to comprehend the chapters in Class 12 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNCERT Class 12 Maths can seem scary at first, but if you plan ahead of time, you can easily conquer your phobia of the subject. NCERT Solutions Class 12 Maths on Infinity Learn is the greatest way to comprehend all of the chapters in Class 12 Maths. All of Infinity Learn's Class 12 Maths solutions include detailed explanations for each topic and subtopic, as well as exercise questions\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<h5><span class=\"ez-toc-section\" id=\"What_is_the_underlying_concept_of_Chapter_8_Application_of_Integrals\"><\/span>What is the underlying concept of Chapter 8 Application of Integrals?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe underlying concept of NCERT Class 12 Maths Chapter 8 Application of Integrals deals with the usage of geometric formulae for calculating the area of different geometric shapes and the area between two curves, area between curve and line, area between arbitrary positions, and trigonometric identities integrals. To get solutions to all exercises, you must refer to NCERT Class 12 Maths Chapter 8 on Infinity Learn.\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 math Class 12, which chapters have been removed?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The CBSE syllabus for Class 12 Maths has been lowered by 30%, according to the new CBSE syllabus. Full chapters have not been eliminated from the CBSE Class 12 Maths syllabus, although portions of each unit have been removed. Download the NCERT Solutions Maths Chapter 8 PDF, which is only accessible on Infinity Learn, to acquire the whole NCERT Solutions Maths Chapter 8 based on the most recent curriculum. For a better understanding, extra important questions are also answered\"\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 will I be able to comprehend the chapters in Class 12 Maths?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"NCERT Class 12 Maths can seem scary at first, but if you plan ahead of time, you can easily conquer your phobia of the subject. NCERT Solutions Class 12 Maths on Infinity Learn is the greatest way to comprehend all of the chapters in Class 12 Maths. All of Infinity Learn's Class 12 Maths solutions include detailed explanations for each topic and subtopic, as well as exercise questions\"\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 is the underlying concept of Chapter 8 Application of Integrals?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The underlying concept of NCERT Class 12 Maths Chapter 8 Application of Integrals deals with the usage of geometric formulae for calculating the area of different geometric shapes and the area between two curves, area between curve and line, area between arbitrary positions, and trigonometric identities integrals. To get solutions to all exercises, you must refer to NCERT Class 12 Maths Chapter 8 on Infinity Learn.\"\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 Class 12 Maths Chapter 8 Application of Integrals Ex 8.1 All of the questions that must be studied [&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 8 Application of Integrals Ex 8.1","_yoast_wpseo_title":"NCERT Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.1","_yoast_wpseo_metadesc":"Free NCERT Solutions for Class 12 Maths Chapter 8 - Applications of Integrals solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-8-application-of-integrals-exercise-8-1\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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