{"id":5903,"date":"2025-08-18T10:45:14","date_gmt":"2025-08-18T05:15:14","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=5903"},"modified":"2025-08-18T10:45:14","modified_gmt":"2025-08-18T05:15:14","slug":"applications-of-integration","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/calculus-and-differeential-equations\/applications-of-integration","title":{"rendered":"Applications of Integration"},"content":{"rendered":"<p style=\"text-align: justify;\">We study three areas where applications of integration is applied<\/p>\n<p style=\"text-align: justify;\"><strong>1.<\/strong> Areas of curves<br \/>\n<strong>2.<\/strong> Length of curves<br \/>\n<strong>3.<\/strong> Volumes of revolution<\/p>\n<h2 style=\"text-align: justify;\">Differential Equations<\/h2>\n<p style=\"text-align: justify;\">Differential equations are fundamental in engineering mathematics since many of the physical laws and relationships between physical quantities appear mathematically in the form of such equations.<\/p>\n<h3 style=\"text-align: justify;\">Definitions<\/h3>\n<p style=\"text-align: justify;\">A differential equation is an equation that involves derivatives or differential coefficients or differentials. Thus, the following are all examples of differential equations.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5904 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/08\/differential-equation.jpg\" alt=\"Differential equation\" width=\"534\" height=\"249\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/08\/differential-equation.jpg 534w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/08\/differential-equation-300x140.jpg 300w\" sizes=\"auto, (max-width: 534px) 100vw, 534px\" \/><\/p>\n<p style=\"text-align: justify;\">An ordinary differential equations is that in which all the differential coefficients all with respect to a single independent variable. Thus the equations (a) to (d) are all ordinary differential equations. (e) is a system of ordinary differential equations.<\/p>\n<p style=\"text-align: justify;\">A partial differential equations is that in which there are two or more independent variables and partial differential coefficients with respect to any of them. The equations (f) and (g) are partial differential equations.<\/p>\n<p style=\"text-align: justify;\">The order of a differential equation is the order of the highest derivative appearing in it. The degree of a differetial equation is the degree of the highest derivative occurring in it, after the equation has been expressed in a form free from radicals and fractions as far as the derivatives are concerned.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study three areas where applications of integration is applied 1. Areas of curves 2. Length of curves 3. Volumes<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1733,5],"tags":[1751,1753,1752],"class_list":["post-5903","post","type-post","status-publish","format-standard","hentry","category-calculus-and-differeential-equations","category-ee","tag-areas-of-curves","tag-differential-equations","tag-volumes-of-revolution"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5903","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=5903"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5903\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}