Problem 47874. Compute an integral of an exponential function

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: 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>

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Last Solution submitted on Jul 24, 2021

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Solution 6153389

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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

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

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!

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Problem 47874. Compute an integral of an exponential function

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Problem 47874. Compute an integral of an exponential function

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