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Math Help - Triple integral problem

  1. #1
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    Triple integral problem

    [IMG]file:///C:/DOCUME%7E1/AWCOLL%7E1/LOCALS%7E1/Temp/moz-screenshot-2.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/AWCOLL%7E1/LOCALS%7E1/Temp/moz-screenshot-3.jpg[/IMG]Hello, I think I am just doing the integration with respect to x incorrectly, can anyone help me out here?

    Evaluate where is the box determined by
    , , and .
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  2. #2
    Junior Member slider142's Avatar
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    Unfortunately, I cannot see your screenshots. By Fubini's theorem, you can integrate this with respect to any variable you choose first. The simplest integral is with respect to z, which returns the same integrand. The next simplest is integrating with respect to x. when we do this, remember that we treat y (and any other variables not dependent on x) as a constant. Thus, our integrand is just like ke^{kx} where k is a constant. This should be a familiar derivative.
    After this integral is done, then the last integral I would do would be y. This is in arbitrary order of simplicity however; since the limits are all constants, you are free to do the integral in whatever order you want without worrying about reparameterizing boundary curves.
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  3. #3
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    Thanks a lot. It was just the fact that I was forgetting to hold y constant at that time when integrating with respect to x. I'm sorry, I know I need to add more detail about where I am having trouble specifically. This goes especially for my other recent post about a similar problem. I will try to update that post and be more specific because I am familiar with these types of problems (I am learning them in a calc 3 course right now) but I just get stuck from time to time at places. Thank you again very much for your help!
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