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Math Help - [SOLVED] finding the double integral of an e^x problem

  1. #1
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    [SOLVED] finding the double integral of an e^x problem

    I have the double integral of....

    ∫∫xye^((x^2)y) dxdy

    the inner integral goes from 0 to 1
    the outer integral goes from 0 to 2

    Do we need to u-sub for this, because I can't see what we need to look for if that's the case.

    if it IS u-sub, this is what I may have:
    u = x^2
    du = 2xdx
    xdx = (1/2)du
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  2. #2
    Senior Member
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    Yes, your substitution is correct.

    \int_0^2 \int_0^1 x \, y \, e^{x^2 y} \, dx \, dy

    Let u=x^2 \implies du = 2x \, dx

    \frac{1}{2} \int_0^2 \int_0^1 y \, e^{u y} \, du \, dy

    = \frac{1}{2} \int_0^2 \left[ e^{u y} \right]_0^1 \, dy

    = \frac{1}{2} \int_0^2 ( e^y - 1 ) \, dy
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  3. #3
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    Thanks! I got the same answer, but it's good to have a second opinion!
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