Problem 51456. Compute an improper integral of a ratio of algebraic functions

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=\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\"/></w:customXmlPr><w:r><w:t>I = \\int_0^\\infty\\frac{x^2dx}{x^4+(a^2+b^2)x^2+a^2b^2</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:customXmlPr><w:r><w:t>a</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:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> are positive real numbers. 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>.</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: 105.083px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5417px; transform-origin: 407px 52.5417px; 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: 152.742px 7.91667px; transform-origin: 152.742px 7.91667px; unicode-bidi: normal; "><span style="">Write a function to compute the following integral:</span></span></div><div style="block-size: 45.0833px; 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 22.5417px; text-align: left; transform-origin: 384px 22.5417px; 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="integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})" style="width: 193px; height: 45px;" width="193" height="45"></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);">a</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);">b</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: 138.217px 7.91667px; transform-origin: 138.217px 7.91667px; unicode-bidi: normal; "><span style=""> are positive real numbers. 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: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

30 Solutions
14 Solvers

Last Solution submitted on Jul 07, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers14

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 51456. Compute an improper integral of a ratio of algebraic functions

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers14

Suggested Problems

More from this Author221

Problem Tags

Community Treasure Hunt

Problem 51456. Compute an improper integral of a ratio of algebraic functions

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers14

Suggested Problems

More from this Author221

Problem Tags

Community Treasure Hunt

Players