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Math Help - double integrals

  1. #1
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    double integrals

    Having trouble figuring these out.

    1. Integral 0 to ln3 integral 0 to ln2 e^x+y dydx

    2. Integral 0 to 1 integral 0 to 1 x over (xy+1)^2 dydx
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  2. #2
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    Are you asking \int_{0}^{ln(3))}e^x dx\int_{0}^{ln(2))}e^ydy ?

    If so, this is 2*1 = 2....

    Remember e^{ln(a)} = a
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  3. #3
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    For second integral, I'm less certain, but here goes:

    \int_{0}^{1}\int_{0}^{1}\frac{xdxdy}{(1+xy)^2} = \int_{0}^{1}dx\int_{0}^{1}\frac{xdy}{(1+xy)^2}.

    For the integral over y, treat x as a constant, which yields:

    \int_{0}^{1}\left ( 1-\frac{1}{1+x} \right )dx..

    Which in turn yields: 1 - ln(2)
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