{"id":4412,"date":"2022-06-13T07:12:54","date_gmt":"2022-06-13T07:12:54","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4412"},"modified":"2022-06-13T07:12:54","modified_gmt":"2022-06-13T07:12:54","slug":"properties-of-integral-calculus","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/13\/properties-of-integral-calculus\/","title":{"rendered":"Properties of Integral Calculus"},"content":{"rendered":"\n<p>Let us study the properties of indefinite integrals to work on them.&nbsp;<\/p>\n\n\n\n<ul><li>The derivative of an integral&nbsp;is the integrand itself. \u222b f(x) dx = f(x) +C<\/li><li>Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent.&nbsp;\u222b [ f(x) dx -g(x) dx] =0<\/li><li>The integral of the sum or difference of a finite number of functions is equal to the sum or difference of the integrals of the individual functions.&nbsp;\u222b [ f(x) dx+g(x) dx] = \u222b f(x) dx +&nbsp;\u222b g(x) dx<\/li><li>The constant is taken outside the integral sign. \u222b k f(x) dx = k \u222b f(x) dx, where k&nbsp;\u2208 R.<\/li><li>The previous two properties are combined to get the form: \u222b [k11f11(x) + k22f22(x) +&#8230; knnfnn(x)] dx = k11\u222b f11(x)dx + k22\u222b f22(x)dx+ &#8230;&nbsp;knn&nbsp;\u222b fnn(x)dx<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Let us study the properties of indefinite integrals to work on them.&nbsp; The derivative of an integral&nbsp;is the integrand itself. \u222b f(x) dx = f(x) +C Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent.&nbsp;\u222b [ f(x) dx -g(x) dx] =0 The integral 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\/4412"}],"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=4412"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4412\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}