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Math Help - Evaluate the integral by reversing the order

  1. #1
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    Evaluate the integral by reversing the order

    Evaluate the integral by reversing the order of integration.
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  2. #2
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    Hello, wvlilgurl!

    Evaluate the integral by reversing the order of integration.

    . \int^2_0 \int^4_{y^2} y\cos(x^2)\,dx\,dy
    The region is bounded by: . \begin{array}{c}y\,=\,2\\ y\,=\,0\end{array}\:\text{ and }\:\begin{array}{c}x\,=\,4 \\ x=y^2\end{array}
    Code:
              |
              |             *
            2 +         *
              |     *:::|
              |  *::::::|
              |*::::::::|
              |:::::::::|
          - - * - - - - * - - -
              |         4

    Reversing the order: . \begin{array}{c} y \,=\,x^{\frac{1}{2}} \\ y \,=\,0\end{array}\:\text{ and }\:\begin{array}{c}x \,=\,4 \\ x\,=\,0 \end{array}

    The integral becomes: . \int^4_0 \int^{x^{\frac{1}{2}}}_0 y\cos(x^2)\,dy\,dx

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  3. #3
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    I got that far but I dont know how to integrate it. Thanks!
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