{"id":69098,"date":"2023-09-01T15:54:00","date_gmt":"2023-09-01T10:24:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69098"},"modified":"2023-11-29T10:33:10","modified_gmt":"2023-11-29T05:03:10","slug":"rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/","title":{"rendered":"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 (Updated for 2023)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-118700\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.8.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8:\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.8.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.8-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8:<\/strong> Solutions PDF is an important reference guide to help students score well in the Class 12 exam. By solving exercise problems on a daily basis, students improve their problem-solving and logical thinking skills. This is important for getting better academic grades. The main goal is to help students self-analyze the areas that require the most practice from the exam point of view. With the help of <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-indefinite-integrals\/\"><strong>RD Sharma Solutions Class 12 Maths Chapter 19<\/strong><\/a> Exercise 19.8, students can solve exercise problems in a short duration clearly.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions For Class 12th\u00a0Maths All Chapters<\/a><\/li>\n<\/ul>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 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\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d7791de852f\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" 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: #000000;color:#000000\" 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-69d7791de852f\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-198-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 PDF:\">Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 PDF:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#access-rd-sharma-solutions-class-12-maths-chapter-19-exercise-198\" title=\"Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8\">Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#rd-sharma-solutions-class-12-maths-chapter-19-exercise-198-important-topics-from-the-chapter\" title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8: Important Topics From The Chapter\">RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8: Important Topics From The Chapter<\/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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#faqs-on-rd-sharma-solutions-class-12-maths-chapter-19-exercise-198\" title=\"FAQs on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8\">FAQs on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#is-rd-sharma-solutions-for-class-12-maths-chapter-19-exercise-198-for-free\" title=\"Is RD Sharma Solutions for Class 12 Maths Chapter 19 Exercise 19.8 for free?\">Is RD Sharma Solutions for Class 12 Maths Chapter 19 Exercise 19.8 for free?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#where-can-i-download-rd-sharma-solutions-class-12-chapter-19-exercise-198-free-pdf\" title=\"Where can I download RD Sharma Solutions Class 12 Chapter 19 Exercise 19.8 free PDF?\">Where can I download RD Sharma Solutions Class 12 Chapter 19 Exercise 19.8 free PDF?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/#are-indefinite-integrals-and-antiderivatives-the-same\" title=\"Are indefinite integrals and Antiderivatives the same?\">Are indefinite integrals and Antiderivatives the same?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-198-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 PDF:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.8.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.8.pdf\">RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.8<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-12-maths-chapter-19-exercise-198\"><\/span>Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-134.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 134\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 135\" \/><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-136.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 136\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-137a.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 137a\" \/><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-137.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 137\" \/><\/p>\n<p><img class=\"\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-141.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 141\" width=\"167\" height=\"54\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-142.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 142\" \/><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-143.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 143\" \/><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-144.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 144\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-145.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 145\" \/><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-146.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 146\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-147.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 147\" \/><\/p>\n<p>Therefore,<\/p>\n<p>= cos (b \u2013 a)x + sin(b \u2013 a) log |sin(x \u2013 b)| + c, where c is an arbitrary constant.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-12-maths-chapter-19-exercise-198-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Some of the essential topics covered in this chapter are listed below.<\/p>\n<ul>\n<li>Definition of primitive or antiderivative<\/li>\n<li>Definition and meaning of indefinite integral<\/li>\n<li>Fundamental integration formulae<\/li>\n<li>Some standard results on integration along with the corollary<\/li>\n<li>Integration of trigonometric functions<\/li>\n<li>Integration of exponential functions<\/li>\n<li>Miscellaneous problems<\/li>\n<li>Geometrical interpretation of indefinite integral<\/li>\n<li>Comparison between differentiation and integration<\/li>\n<li>Methods of integration<\/li>\n<li>Integration by substitution<\/li>\n<li>Some standard results<\/li>\n<li>Evaluation of integrals by using trigonometric substitutions<\/li>\n<li>Some special integrals<\/li>\n<li>Integration by parts<\/li>\n<li>Some important integrals along with the arms<\/li>\n<li>Integration of rational algebraic functions by using partial fractions\n<ul>\n<li>When the denominator is expressible as a product of distinct linear factors<\/li>\n<li>When the denominator contains some repeating linear factors<\/li>\n<li>The denominator contains irreducible quadratic factors<\/li>\n<\/ul>\n<\/li>\n<li>Integration of some special irrational algebraic functions<\/li>\n<\/ul>\n<p>We have included all the information regarding <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8. If you have any queries feel free to ask in the comment section.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-12-maths-chapter-19-exercise-198\"><\/span><strong>FAQs on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630500726296\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-solutions-for-class-12-maths-chapter-19-exercise-198-for-free\"><\/span>Is RD Sharma Solutions for Class 12 Maths Chapter 19 Exercise 19.8 for free?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, You can get RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 for free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630500882093\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-solutions-class-12-chapter-19-exercise-198-free-pdf\"><\/span>Where can I download RD Sharma Solutions Class 12 Chapter 19 Exercise 19.8 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Solutions Class 12 Chapter 19 Exercise 19.8 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630500925133\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-indefinite-integrals-and-antiderivatives-the-same\"><\/span>Are indefinite integrals and Antiderivatives the same?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>An antiderivative of a function f(x) is a function whose derivative is equal to f(x).\u00a0An indefinite integral is an integral written without terminals; it simply asks us to find a general antiderivative of the integrand.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8: Solutions PDF is an important reference guide to help students score well in the Class 12 exam. By solving exercise problems on a daily basis, students improve their problem-solving and logical thinking skills. This is important for getting better academic grades. The main goal is &#8230; <a title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 (Updated for 2023)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-8\/\" aria-label=\"More on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.8 (Updated for 2023)\">Read more<\/a><\/p>\n","protected":false},"author":236,"featured_media":118700,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3429,73223,73664,76740],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69098"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/236"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=69098"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69098\/revisions"}],"predecessor-version":[{"id":513790,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69098\/revisions\/513790"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/118700"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}