Problem 47874. Compute an integral of an exponential function

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>This problem builds on </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/47673-area-under-standard-normal-curve\"><w:r><w:t>Cody Problem 47673</w:t></w:r></w:hyperlink><w:r><w:t>, in which Mehmet OZC asks us to compute the area under the standard normal curve. Write a function to compute the following integral:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>y = \\int_0^a \\exp(-b x^p) dx</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You may not use </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>integral</w:t></w:r><w:r><w:rPr/><w:t> or </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>quad</w:t></w:r><w:r><w:rPr/><w:t>. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 125px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 62.5px; transform-origin: 407px 62.5px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 7.91667px; transform-origin: 72.3583px 7.91667px; unicode-bidi: normal; "><span style="">This problem builds on </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/47673-area-under-standard-normal-curve"><span style=""><span style="">Cody Problem 47673</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 225.583px 7.91667px; transform-origin: 225.583px 7.91667px; unicode-bidi: normal; "><span style="">, in which Mehmet OZC asks us to compute the area under the standard normal curve. Write a function to compute the following integral:</span></span></div><div style="block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" style="width: 131px; height: 44px;" width="131" height="44"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.8083px 7.91667px; transform-origin: 53.8083px 7.91667px; unicode-bidi: normal; "><span style="">You may not use </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">integral</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; "><span style=""> or </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">quad</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">. </span></span></div></div></div>

Solve

Solution Stats

22 Solutions
4 Solvers

Last Solution submitted on Jul 24, 2021

Last 200 Solutions

Problem Comments

Solution Comments

Solution 6153389

3 Comments

3 Comments

Dyuman Joshi on 7 Aug 2021

This should work right? I tried simplifying this as well but not sure why it fails

ChrisR on 4 Sep 2021 at 15:29

Dyuman, I have a different set of arguments for the first function in your code. I will need to dig into it to figure out the differences.

Dyuman Joshi on 4 Sep 2021 at 17:59

Yeah I noticed that too in Tim's answer. If you find any differences, please let me know, it will be very helpful, Thank you!

Problem Recent Solvers4

Problem Tags

integration special functions

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 47874. Compute an integral of an exponential function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author129

Problem Tags

Community Treasure Hunt

Problem 47874. Compute an integral of an exponential function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author129

Problem Tags

Community Treasure Hunt

Players