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Math Help - double integral

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    double integral

    using polar coordinates evaluate the double integral R=sin(x^2+y^2) dA where R is the region 1 less than or equal to x^2+y^2 less than or equal to 64.


    Using polar coordinates evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=144 and x^2-12x+y^2=0.
    Last edited by karnold9; July 10th 2008 at 08:34 AM.
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    Quote Originally Posted by karnold9 View Post
    using polar coordinates evaluate the double integral R=sin(x^2+y^2) dA where R is the region 1 less than or equal to x^2+y^2 less than or equal to 64.


    Using polar coordinates evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=144 and x^2-12x+y^2=0.
    \iint_D \sin(x^2+y^2)dA=\int_{0}^{8}\int_{0}^{2\pi}r\sin(r  ^2)d\theta dr

    Did you draw a graph for the 2nd one. If not it will really help. Here it is.

    double integral-capture.jpg

    Note this can be done with out calculus. Good luck.
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