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Math Help - Double Integral Help

  1. #1
    GmasterFlash13
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    Double Integral Help

    I have a question in my Prob & Stat course that deals with double integration, and it's been two years since Calc III and I really don't remember exactly how to solve one. Here's the question:

    The first part isn't really a double integral, but will eventually lead to one:

    Integral ( xe^(-x(1+y) ) ) dy

    Essentially, I am not sure how to integrate that for y. The bounds don't really matter in this case, I need to know the y-integration.

    To anyone who can help, it'd be much appreciated. Thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by GmasterFlash13 View Post
    I have a question in my Prob & Stat course that deals with double integration, and it's been two years since Calc III and I really don't remember exactly how to solve one. Here's the question:

    The first part isn't really a double integral, but will eventually lead to one:

    Integral ( xe^(-x(1+y) ) ) dy

    Essentially, I am not sure how to integrate that for y. The bounds don't really matter in this case, I need to know the y-integration.

    To anyone who can help, it'd be much appreciated. Thanks.
    Your integral is:
    Int(dxdy*xe^(-x-xy)) = Int(dx*xe^(-x) * Int(dy*e^(-xy)) )
    where I have split the integral into components.

    The second integral (the one you are interested in) can be simply done by assuming x is a constant (it doesn't vary as y varies anyway), so
    Int(dy*e^(-xy)) = 1/(-x) * e^(-xy)
    where I have neglected the integration constant.

    -Dan
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