Problem 51137. Compute an integral of a product of sinusoids

Created by ChrisR

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<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>

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ChrisR on 2 Apr 2021

Nice

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ChrisR on 26 Mar 2021

I'm setting a target for Tim and others.

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integration sinusoid special functions

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Problem 51137. Compute an integral of a product of sinusoids

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Problem 51137. Compute an integral of a product of sinusoids

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