{"id":4391,"date":"2022-06-13T06:50:48","date_gmt":"2022-06-13T06:50:48","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4391"},"modified":"2022-06-13T06:50:48","modified_gmt":"2022-06-13T06:50:48","slug":"trapezoidal-rule-formula","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/13\/trapezoidal-rule-formula\/","title":{"rendered":"Trapezoidal Rule Formula"},"content":{"rendered":"\n<p>We apply the trapezoidal rule formula to solve a definite integral by calculating the area under a curve by dividing the total area into little\u00a0trapezoids\u00a0rather than\u00a0rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions. The trapezoidal rule takes the average of the left and the right sum.<\/p>\n\n\n\n<p>Let y = f(x) be\u00a0continuous\u00a0on [a, b]. We divide the interval [a, b] into n equal subintervals, each of width, h = (b &#8211; a)\/n,<\/p>\n\n\n\n<p>such that a = x<sub>0<\/sub>&nbsp;&lt; x<sub>1<\/sub>&nbsp;&lt; x<sub>2<\/sub>&nbsp;&lt; \u22ef &lt; x<sub>n<\/sub>&nbsp;= b<\/p>\n\n\n\n<p><strong>Area = (h\/2) [y<sub>0&nbsp;<\/sub>+ 2 (y<sub>1&nbsp;<\/sub>+ y<sub>2&nbsp;<\/sub>+ y<sub>3&nbsp;<\/sub>+ &#8230;.. + y<sub>n-1<\/sub>) + y<sub>n<\/sub>]<\/strong><\/p>\n\n\n\n<p>where,<\/p>\n\n\n\n<ul><li>y<sub>0<\/sub>, y<sub>1<\/sub>,y<sub>2<\/sub>\u2026. are the values of function at x = 1, 2, 3\u2026.. respectively.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/06\/formula-of-trapezoidal-rule-1619630072-1623752119-1020x1024.png\" alt=\"\" class=\"wp-image-4392\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>We apply the trapezoidal rule formula to solve a definite integral by calculating the area under a curve by dividing the total area into little\u00a0trapezoids\u00a0rather than\u00a0rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions. The trapezoidal rule takes the average of the left and 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":[874],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4391"}],"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=4391"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4391\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}