{"id":69093,"date":"2023-08-31T19:21:00","date_gmt":"2023-08-31T13:51:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69093"},"modified":"2023-11-16T10:43:59","modified_gmt":"2023-11-16T05:13:59","slug":"rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-5","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-5\/","title":{"rendered":"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 (2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-118644\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.5.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.5.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.5-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5<\/strong>: Solutions PDF is an important reference guide to help students score well in the Class 12 exam. By solving exercise problems from RD Sharma Solutions 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.&nbsp;<\/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&nbsp;Maths 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-69e19f12d39ba\" 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-69e19f12d39ba\"><\/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-19-5\/#download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-195-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 PDF:\">Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 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-19-5\/#access-solutions-rd-sharma-class-12-maths-chapter-19-exercise-195\" title=\"Access Solutions RD Sharma Class 12 Maths Chapter 19 Exercise 19.5\">Access Solutions RD Sharma Class 12 Maths Chapter 19 Exercise 19.5<\/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-19-5\/#rd-sharma-solutions-class-12-maths-chapter-19-exercise-195-important-topics-from-the-chapter\" title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5: Important Topics From The Chapter\">RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5: 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-19-5\/#faq-rd-sharma-solutions-class-12-maths-chapter-19-exercise-195\" title=\"FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5\">FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5<\/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-19-5\/#how-many-types-of-integral-are-there\" title=\"How many types of Integral are there? \">How many types of Integral are there? <\/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-19-5\/#are-indefinite-integrals-and-antiderivatives-the-same\" title=\"Are indefinite integrals and Antiderivatives the same?\">Are indefinite integrals and Antiderivatives the same?<\/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-19-5\/#can-i-download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-195-pdf-free\" title=\"Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 PDF Free? \">Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 PDF Free? <\/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-19-5\/#how-indefinite-integrals-are-represented\" title=\"How Indefinite Integrals are represented? \">How Indefinite Integrals are represented? <\/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-19-5\/#how-indefinite-integral-and-antiderivative-are-related\" title=\"How indefinite integral and antiderivative are related? \">How indefinite integral and antiderivative are related? <\/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-195-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 PDF:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/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-19.5.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-19.5.pdf\" target=\"_blank\" rel=\"noopener\">RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.5<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-solutions-rd-sharma-class-12-maths-chapter-19-exercise-195\"><\/span>Access Solutions RD Sharma Class 12 Maths Chapter 19 Exercise 19.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Indefinite Integrals Ex 19.5 Q1<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/3\/2193\/32853575746_ff8db9caa4_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q1\" width=\"570\" height=\"650\"><br><strong>Indefinite Integrals Ex 19.5 Q2<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/1\/685\/32514034290_64ebb24ae4_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q2\" width=\"534\" height=\"184\"><br><strong>Indefinite Integrals Ex 19.5 Q3<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/1\/667\/32514034260_4df756ae3e_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q3\" width=\"403\" height=\"392\"><br><strong>Indefinite Integrals Ex 19.5 Q4<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/3\/2071\/32514034220_2a048f3aa6_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q4\" width=\"470\" height=\"686\"><br><strong>Indefinite Integrals Ex 19.5 Q5<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/3\/2362\/32514034060_78c2f4fe1d_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q5\" width=\"471\" height=\"685\"><br><strong>Indefinite Integrals Ex 19.5 Q6<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/1\/696\/32740830482_cde6a5b16e_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q6\" width=\"478\" height=\"632\"><br><strong>Indefinite Integrals Ex 19.5 Q7<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/1\/315\/32514034000_66e7ec5327_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q7\" width=\"318\" height=\"469\"><br><strong>Indefinite Integrals Ex 19.5 Q8<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/3\/2196\/32514033960_1a20a4dc6d_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q8\" width=\"408\" height=\"567\"><br><strong>Indefinite Integrals Ex 19.5 Q9<\/strong><br><img src=\"https:\/\/c1.staticflickr.com\/1\/416\/32514034500_78ff11401a_o.png\" alt=\"RD-Sharma-Class-12-Solutions-Chapter-19-indefinite-integrals-Ex-19.5-Q9\" width=\"393\" height=\"748\"><\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-12-maths-chapter-19-exercise-195-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Some of the essential topics covered in &nbsp;<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 19.5<\/span>&nbsp;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>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 19.5. If you have any doubt feel free to ask in the comment section.&nbsp;<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faq-rd-sharma-solutions-class-12-maths-chapter-19-exercise-195\"><\/span>FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5<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-1629812889152\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-types-of-integral-are-there\"><\/span>How many types of Integral are there? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Definite Integrals and Indefinite Integrals. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629812922586\" 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 id=\"faq-question-1629812923880\" 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-195-pdf-free\"><\/span>Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 PDF Free? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, You can download D Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 PDF free. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629812986858\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-indefinite-integrals-are-represented\"><\/span>How Indefinite Integrals are represented? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>It is visually represented as an integral symbol, a function, and then a dx at the end.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629812987737\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-indefinite-integral-and-antiderivative-are-related\"><\/span>How indefinite integral and antiderivative are related? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The indefinite integral is an easier way to symbolize taking the antiderivative.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5: Solutions PDF is an important reference guide to help students score well in the Class 12 exam. By solving exercise problems from RD Sharma Solutions on a daily basis, 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 19.5 (2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-5\/\" aria-label=\"More on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.5 (2024)\">Read more<\/a><\/p>\n","protected":false},"author":244,"featured_media":118644,"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":[3429,73223,73664,76737],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69093"}],"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=69093"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69093\/revisions"}],"predecessor-version":[{"id":507983,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69093\/revisions\/507983"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/118644"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}