Problem 51137. Compute an integral of a product of sinusoids

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>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:attr w:name=\"altTextString\" w:val=\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\"/></w:customXmlPr><w:r><w:t>I = \\int_0^\\pi \\sin^mx\\cos^nxdx</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>where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"m\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> are integers. 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: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:t> but other functions are allowed.</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: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; "><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: 150.8px 7.91667px; transform-origin: 150.8px 7.91667px; unicode-bidi: normal; "><span style="">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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" alt="I = integral(sin(x)^m cos(x)^n, {x,0,pi})" style="width: 139px; height: 44px;" width="139" 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: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; "><span style="">where </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">m</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: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "><span style=""> and </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</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: 96.5917px 7.91667px; transform-origin: 96.5917px 7.91667px; unicode-bidi: normal; "><span style=""> are integers. 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: 99.1917px 7.91667px; transform-origin: 99.1917px 7.91667px; unicode-bidi: normal; "><span style=""> but other functions are allowed.</span></span></div></div></div>

Solve

Solution Stats

15 Solutions
6 Solvers

Last Solution submitted on Apr 05, 2021

Last 200 Solutions

Problem Comments

Solution Comments

Solution 5239389

1 Comment

1 Comment

ChrisR on 2 Apr 2021

Nice

Solution 5176471

1 Comment

1 Comment

ChrisR on 26 Mar 2021

I'm setting a target for Tim and others.

Problem Recent Solvers6

Problem Tags

integration sinusoid special functions

Community Treasure Hunt

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

Start Hunting!

Problem 51137. Compute an integral of a product of sinusoids

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers6

Suggested Problems

More from this Author129

Problem Tags

Community Treasure Hunt

Problem 51137. Compute an integral of a product of sinusoids

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers6

Suggested Problems

More from this Author129

Problem Tags

Community Treasure Hunt

Players