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Math Help - Double Integral Question

  1. #1
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    Double Integral Question

    Textbook Problem: Replace the given iterated integral by an equivalent one with the order of integration reversed.


    \int_0^2{\int_0^{x^2}{x^3 y \, dy} \, dx}


    I came up with the answer:


    \int_0^4{\int_{\sqrt{y}}^2{x^3 y \, dx} \, dy}


    The answer section of the textbook says:


    \int_0^4{\int_{\sqrt{y}}^y{x^3 y \, dx} \, dy}


    The upper limit of the interval of integration is different. Did I make a mistake or did the textbook make a mistake?


    I would like to make sure that I am doing this stuff correctly.
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  2. #2
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    Re: Double Integral Question

    I believe that you are correct.
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