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Math Help - Double Integrals

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    Double Integrals

    Evaluate the integral by reversing the order of integration.

    The integrand is e^x^2 with x limits of 8y to 8 and y limits of 0 to 1
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    Hello,
    Quote Originally Posted by Snooks02 View Post
    Evaluate the integral by reversing the order of integration.

    The integrand is e^x^2 with x limits of 8y to 8 and y limits of 0 to 1
    \int_0^1 \int_{8y}^8 e^{x^2} ~ dx ~ dy

    8y \leq x \leq 8
    0 \leq y \leq 1

    8y \leq x \implies y \leq \tfrac x8 and 0 \leq y. Hence \boxed{0 \leq y \leq \tfrac x8}

    Similarly, we get \boxed{0 \leq x \leq 8}


    So the new integral is :

    \int_0^8 \int_0^{x/8} e^{x^2} ~dy ~dx=\int_0^8 e^{x^2} \left(\int_0^{x/8} dy \right) ~dx
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