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Math Help - Double integral in polar coordinates

  1. #1
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    Double integral in polar coordinates

    Hi

    I need help with the this following double integral. I know how to carry out double integrals but in this polar coordinates double integral case i am not sure of what limits to use.

    Evaluate the double integral

    \iint_{D}ydA where D is the region in the first quadrant that is outside the circle r=2and inside the cardioid r=2(1+cos\theta).

    any help is appreichated

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  2. #2
    MHF Contributor Calculus26's Avatar
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    The region is symmetric about the x-axis and y is positive above and negative below so the integral will be 0.

    See attachment
    Attached Thumbnails Attached Thumbnails Double integral in polar coordinates-poloar.jpg  
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  3. #3
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    its only to do with the first quadrant. So will the limits still be pi/2 and -pi/2 ?
    and will the answer be 0 ?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Missed the first quadrant part--- limits will be o to pi/2 and the answer will be 22/3 as in the attachment
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