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Simple question about an integral

  1. Feb 24, 2013 #1
    This is part of an example solution to a problem about integrating a function in a [0,1]x[0,1]x[0,1] cube. I just don't understand how the midst function is integrated like in the attached picture. This is the same integral in wolfram alpha and it gives a different solution:
    http://www.wolframalpha.com/input/?i=intg((yz^2)*e^(-xyz))
     

    Attached Files:

  2. jcsd
  3. Feb 24, 2013 #2

    Zondrina

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    If you're choosing to integrate over a nice cube, the order of integration does not matter I believe.

    Your integration for dx is wrong. You may want to re-integrate it.
     
    Last edited: Feb 24, 2013
  4. Feb 24, 2013 #3
    You mean the integral in the attachment is wrong? It's part of an example solution not done by me so I thought it would be right but it would help a lot to know that there is an error in the example solution.
     
  5. Feb 24, 2013 #4

    Zondrina

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    Indeed, your first integration is really :

    ##\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} yz^2e^{-xyz}dxdydz##
    ##= \int_{0}^{1} \int_{0}^{1} yz^2\int_{0}^{1} e^{-xyz}dxdydz##
    ##= \int_{0}^{1} \int_{0}^{1} z - ze^{-yz}dydz##

    The rest shouldn't be too hard :)
     
  6. Feb 24, 2013 #5
    Ok thanks, it's clear now
     
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