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Thread: Simplifying a tripple integral

  1. #1
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    Simplifying a tripple integral

    Hello, I am trying to solve an integral but it quickly gets crowded with too many terms... (once you start solving it you'll see what I mean) I was wondering if there is a way to make computations simpler.
    $\displaystyle
    \int^1_0\int^{1-u}_0\int^{1-u-v}_0 8uvw\,dw\,dv\,du
    $
    Thanks in advance
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    Re: Simplifying a tripple integral

    Quote Originally Posted by nuebie View Post
    Hello, I am trying to solve an integral but it quickly gets crowded with too many terms... (once you start solving it you'll see what I mean) I was wondering if there is a way to make computations simpler.
    $\displaystyle
    \int^1_0\int^{1-u}_0\int^{1-u-v}_0 8uvw\,dw\,dv\,du
    $
    Thanks in advance
    Without seeing your work how can we tell if you could have done it easier? It looks straightforward enough, just polynomials.
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    Re: Simplifying a tripple integral

    Hi, yes it's pretty straightforward. It goes like:
    $\displaystyle
    \int^1_0\int^{1-u}_0\int^{1-u-v}_0(8uvw)\mbox{ }dw\,dv\,du = \int^1_0\int^{1-u}_0 4uv\Big[w^2\Big]^{1-u-v}_0 \mbox{ }dv\,du = \int^1_0\int^{1-u}_0 4uv(1-u-v)^2 \mbox{ }dv\,du
    $
    so far so good and as soon as you start expanding it becomes long and ugly, then you integrate again and get even more terms. I mean, it's not difficult but tedious and it's easy to make accidental mistakes. That's why I was asking for a more compact way to do it.
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    Member Walagaster's Avatar
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    Re: Simplifying a tripple integral

    Yes, it's pretty much grunt work. Once you understand integration such problems are a waste of time. If you decide to push it through to the end, the answer is $\frac 1 {90}$ if that is any help. I let Maple do the grunt work.
    Thanks from nuebie
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    Re: Simplifying a tripple integral

    Quote Originally Posted by Walagaster View Post
    Yes, it's pretty much grunt work. Once you understand integration such problems are a waste of time. If you decide to push it through to the end, the answer is $\frac 1 {90}$ if that is any help. I let Maple do the grunt work.
    I agree that it's a waste of time, but I need this one for an assignment problem, so I guess I gotta get through it Thank you!
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