{"id":69114,"date":"2021-08-25T17:21:00","date_gmt":"2021-08-25T11:51:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69114"},"modified":"2021-08-27T13:29:36","modified_gmt":"2021-08-27T07:59:36","slug":"rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-15","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-15\/","title":{"rendered":"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 (2021)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-119062\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.15.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.15.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.15-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15<\/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 from RD Sharma Solutions, students improve their problem solving and logical thinking skills. This is important for getting better academic grades.\u00a0<\/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-69e78e12f32df\" 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-69e78e12f32df\"><\/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-19-15\/#download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 PDF:\">Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 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-19-15\/#access-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915\" title=\"Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15\">Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15<\/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-19-15\/#rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-important-topics-from-the-chapter\" title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15: Important Topics From The Chapter\">RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15: 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-19-15\/#faq-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915\" title=\"FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15\">FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15<\/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-19-15\/#is-rd-sharma-enough-for-board-exams-preparation\" title=\"Is RD Sharma enough for board exams preparation? \">Is RD Sharma enough for board exams preparation? <\/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-19-15\/#can-i-download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-pdf-free\" title=\"Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 PDF free? \">Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 PDF free? <\/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-19-15\/#what-are-the-properties-of-indefinite-integrals\" title=\"What are the properties of indefinite integrals?\">What are the properties of indefinite integrals?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-15\/#what-are-the-important-topics-included-in-rd-sharma-class-12-maths-solutions-chapter-19-exercise-1915\" title=\"What are the important topics included in RD Sharma Class 12 Maths Solutions Chapter 19 Exercise 19.15? \">What are the important topics included in RD Sharma Class 12 Maths Solutions Chapter 19 Exercise 19.15? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-15\/#can-i-open-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-on-any-device\" title=\"Can I open RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 on any device? \">Can I open RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 on any device? <\/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-1915-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 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\/08\/RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.15.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.15.pdf\">RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.15<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915\"><\/span>Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Indefinite Integrals Ex 19.15 Q1<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/3\/2552\/32516323600_fe8637fb4b_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.15-Q1\" width=\"514\" height=\"546\" \/><br \/><strong>Indefinite Integrals Ex 19.15 Q2<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/1\/685\/32516323440_ae36d2f434_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.15-Q2\" width=\"454\" height=\"389\" \/><br \/><strong>Indefinite Integrals Ex 19.15 Q3<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/1\/455\/32081833533_46bf4f4d68_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.15-Q3\" width=\"402\" height=\"548\" \/><br \/><strong>Indefinite Integrals Ex 19.15 Q4<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/3\/2119\/32516323200_07c5cdb0f9_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.15-Q4\" width=\"507\" height=\"654\" \/><br \/><strong>Indefinite Integrals Ex 19.15 Q5<\/strong><br \/><img src=\"https:\/\/c1.staticflickr.com\/3\/2678\/32516323680_a04bed79dd_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.15-Q5\" width=\"639\" height=\"186\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Some of the essential topics covered in \u00a0<span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;RD Sharma Solutions Class 12 Maths Chapter 19 \u2013 Indefinite Integrals&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:5053,&quot;3&quot;:{&quot;1&quot;:0},&quot;5&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;6&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;7&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;8&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;10&quot;:2,&quot;11&quot;:0,&quot;12&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-indefinite-integrals\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 12 Maths Chapter 19 \u2013 Indefinite Integrals<\/a> Exercise 19.15<\/span> 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 theorems<\/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>\u00a0<\/p>\n<p>We have included all the information regarding <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a>\u00a0RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15. If you have any query feel free to ask in the comment section.\u00a0<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faq-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915\"><\/span>FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15<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-1629883522354\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-enough-for-board-exams-preparation\"><\/span>Is RD Sharma enough for board exams preparation? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>RD Sharma is a good book if you want to practice various types of questions. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629883627039\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-pdf-free\"><\/span>Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 PDF free? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, RD Sharma Class 12 Maths Solutions Chapter 19 Exercise 19.15 PDF free. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629883728736\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-properties-of-indefinite-integrals\"><\/span>What are the properties of indefinite integrals?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The indefinite integral of the sum of two functions is equal to the sum of the integrals. The indefinite integral of the difference of two functions is equal to the difference of the integrals.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629883730114\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-important-topics-included-in-rd-sharma-class-12-maths-solutions-chapter-19-exercise-1915\"><\/span>What are the important topics included in RD Sharma Class 12 Maths Solutions Chapter 19 Exercise 19.15? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can refer to the above article to get the important topics for RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629891602274\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-open-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1915-on-any-device\"><\/span>Can I open RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 on any device? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, you can open RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 on any device. <\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15: 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 from RD Sharma Solutions, students improve their problem solving and logical thinking skills. This is important for getting better academic &#8230; <a title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 (2021)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-15\/\" aria-label=\"More on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.15 (2021)\">Read more<\/a><\/p>\n","protected":false},"author":244,"featured_media":119062,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73716,73411,2985,73410],"tags":[3429,73223,73664,76748],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69114"}],"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\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=69114"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69114\/revisions"}],"predecessor-version":[{"id":120394,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69114\/revisions\/120394"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/119062"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}