{"id":4398,"date":"2022-06-13T06:59:34","date_gmt":"2022-06-13T06:59:34","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4398"},"modified":"2022-06-13T06:59:34","modified_gmt":"2022-06-13T06:59:34","slug":"examples-using-trapezoidal-rule","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/13\/examples-using-trapezoidal-rule\/","title":{"rendered":"Examples Using Trapezoidal Rule"},"content":{"rendered":"\n<pre class=\"wp-block-code\"><code>Example 1: <\/code><\/pre>\n\n\n\n<ol><li>Find the area under the curve using trapezoidal rule formula which passes through the following points:x00.511.5y56911  <\/li><\/ol>\n\n\n\n<pre class=\"wp-block-code\"><code>Solution:<\/code><\/pre>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p> y<sub>0<\/sub>\u00a0= 5<br>y<sub>1<\/sub>= 6<br>y<sub>2<\/sub>= 9<br>y<sub>3<\/sub>= 11<br>h = (0.5 &#8211; 0) = (1 &#8211; 0.5) = (1.5 &#8211; 1) = 0.5<\/p>\n\n\n\n<p>Using Trapezoidal rule formula,Area = (h\/2) [y<sub>0\u00a0<\/sub>+ y<sub>n\u00a0<\/sub>+ 2(y<sub>1\u00a0<\/sub>+ y<sub>2\u00a0<\/sub>+ y<sub>3\u00a0<\/sub>+ &#8230;.. + y<sub>n-1<\/sub>)] <\/p>\n\n\n\n<p>=(.5\/2) [5 + 11 + 2 (6 + 9)]<\/p>\n\n\n\n<p>= 0.25 [16+30]= 0.25 [46]= 11.5<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>Answer:\u00a0<\/strong><\/code><\/pre>\n\n\n\n<p><strong>Therefore, the area under the curve is 11.5 sq units.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>Example 2:\u00a0<\/strong> <\/code><\/pre>\n\n\n\n<p>Using Trapezoidal Rule Formula find the area under the curve y = x<sup>2<\/sup>\u00a0between x = 0 and x = 4 using the step size of 1. <\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>Solution:<\/strong><\/code><\/pre>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p> y = x<sup>2<\/sup><br>h = 1<\/p>\n\n\n\n<p>Find the values of \u2018y\u2019 for different values of \u2018x\u2019 by putting the value of \u2018x\u2019 in the equation <\/p>\n\n\n\n<p>y = x<sup>2<\/sup>X01234y = x<sub>2<\/sub>y<sub>0<\/sub>\u00a0= 0y<sub>1<\/sub>\u00a0= 1y<sub>2<\/sub>\u00a0= 4y<sub>3<\/sub>\u00a0= 9y<sub>4<\/sub>\u00a0= 16<\/p>\n\n\n\n<p>Using Trapezoidal rule:<\/p>\n\n\n\n<p>Area = (h\/2) [y<sub>0\u00a0<\/sub>+ y<sub>n\u00a0<\/sub>+ 2 (y<sub>1\u00a0<\/sub>+ y<sub>2\u00a0<\/sub>+ y<sub>3\u00a0<\/sub>+ &#8230;.. + y<sub>n-1<\/sub>)]<\/p>\n\n\n\n<p>= (1\/2) [0 + 16 + 2 (1 + 4 + 9)]= 0.5 [16 + 28]<\/p>\n\n\n\n<p>= 22<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>Answer:\u00a0<\/strong><\/code><\/pre>\n\n\n\n<p>Therefore, the area under the curve is 22 sq units.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>Example 3:\u00a0<\/strong><\/code><\/pre>\n\n\n\n<p>Find the area under the curve using the trapezoidal rule formula which passes through the following points:<\/p>\n\n\n\n<p>x00.511.5  <\/p>\n\n\n\n<p>y471015<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> <strong>Solution: <\/strong><\/code><\/pre>\n\n\n\n<p>Given: y<sub>0\u00a0<\/sub>= 4<br>y<sub>1<\/sub>\u00a0= 7<br>y<sub>2<\/sub>\u00a0= 10<br>y<sub>3<\/sub>\u00a0= 15<br>h = (0.5 &#8211; 0) = (1 &#8211; 0.5) = (1.5 &#8211; 1) = 0.5<\/p>\n\n\n\n<p>Using Trapezoidal formula:<\/p>\n\n\n\n<p>Area = (h\/2) [y<sub>0\u00a0<\/sub>+ y<sub>n\u00a0<\/sub>+ 2 (y<sub>1\u00a0<\/sub>+ y<sub>2\u00a0<\/sub>+ y<sub>3\u00a0<\/sub>+ &#8230;.. + y<sub>n-1<\/sub>)]= (0.5\/2) [4 + 15 + 2 (7 + 10)]<\/p>\n\n\n\n<p>= 0.25 [19 + 34]= 0.25 [53]<\/p>\n\n\n\n<p>= 13.25<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>Answer:\u00a0<\/strong><\/code><\/pre>\n\n\n\n<p>Therefore, the area under the curve is 13.25 sq units.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the area under the curve using trapezoidal rule formula which passes through the following points:x00.511.5y56911 Given: y0\u00a0= 5y1= 6y2= 9y3= 11h = (0.5 &#8211; 0) = (1 &#8211; 0.5) = (1.5 &#8211; 1) = 0.5 Using Trapezoidal rule formula,Area = (h\/2) [y0\u00a0+ yn\u00a0+ 2(y1\u00a0+ y2\u00a0+ y3\u00a0+ &#8230;.. + yn-1)] =(.5\/2) [5 + 11 + [&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\/4398"}],"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=4398"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4398\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}