{"id":4418,"date":"2022-06-13T07:17:51","date_gmt":"2022-06-13T07:17:51","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4418"},"modified":"2022-06-13T07:17:51","modified_gmt":"2022-06-13T07:17:51","slug":"applications-of-integral-calculus","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/13\/applications-of-integral-calculus\/","title":{"rendered":"Applications of Integral Calculus"},"content":{"rendered":"\n<p>Using integration, we can find the distance given the velocity. Definite integrals form the powerful tool to find the area under simple curves, the area bounded by a curve and a line, the\u00a0area between two curves, the volume of the solids. The displacement and motion problems also find their\u00a0applications of integrals. The area of the region enclosed between two curves y = f(x) and y = g(x) and the lines x =a, x =b is given by<\/p>\n\n\n\n<p>Area =&nbsp;b\u222ba(f(x)\u2212g(x))dx\u222bab(f(x)\u2212g(x))dx<\/p>\n\n\n\n<p>Let us find the area bounded by the curve y = x and y = x<sup>2&nbsp;<\/sup>that intersect at (0,0)and (1,1).<\/p>\n\n\n\n<p>The given curves are that of a line and a parabola. The area bounded by the curves =&nbsp;1\u222b0(y2\u2212y1)dx\u222b01(y2\u2212y1)dx<\/p>\n\n\n\n<p>Area =&nbsp;1\u222b0(x\u2212x2)dx\u222b01(x\u2212x2)dx<\/p>\n\n\n\n<p>= x<sup>2&nbsp;<\/sup>\/2- x&nbsp;<sup>3<\/sup>\/3<\/p>\n\n\n\n<p>= 1\/2-1\/3<\/p>\n\n\n\n<p>= 1\/6 sq units.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Using integration, we can find the distance given the velocity. Definite integrals form the powerful tool to find the area under simple curves, the area bounded by a curve and a line, the\u00a0area between two curves, the volume of the solids. The displacement and motion problems also find their\u00a0applications of integrals. The area of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[865],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4418"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4418"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4418\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}