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Math Help - evaluate this impossible integral

  1. #1
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    evaluate this impossible integral

    evaluate this impossible integral
    \int_0^1\int_{3y}^3 e^{x^2}dxdy
    i think there's some way to rearrange this to make it possible, but i don't know how
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  2. #2
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    Quote Originally Posted by Rubberduckzilla View Post
    evaluate this impossible integral
    \int_0^1\int_{3y}^3 e^{x^2}dxdy
    i think there's some way to rearrange this to make it possible, but i don't know how
    Reverse the order of integration.

    Looking at the limits on the integration we have

    0 \leq y \leq 1 and 3y \leq x \leq 3.


    Some rearrangement gives

    0 \leq y \leq \frac{1}{3}x and 0 \leq x \leq 3.


    So the integral becomes

    \int_0^3{\int_0^{\frac{1}{3}x}{e^{x^2}\,dy}\,dx}
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