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Math Help - green's theorem

  1. #1
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    Exclamation green's theorem

    using green's theorem, verify that the area enclosed by the ellipse (x^2)/(a^2)+ (y^2)/(b^2)=1 is given by a*b*pi

    how do i do this? i've tried many times and don't even get the answer a*b*pi any help would be great thanks
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  2. #2
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    Quote Originally Posted by calc626 View Post
    using green's theorem, verify that the area enclosed by the ellipse (x^2)/(a^2)+ (y^2)/(b^2)=1 is given by a*b*pi

    how do i do this? i've tried many times and don't even get the answer a*b*pi any help would be great thanks
    Via Green's theorem

    \frac{1}{2} \oint \limits_c -y \,dx + x\,dy = \iint \limits_R dA with the latter the area of the region R.

    Then let x = a \cos \theta and y = b \sin \theta and compute the line integral.
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    hmm that's what i've been trying but have not been getting the right answer somehow. is the integral from 0 to 2pi?
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    Quote Originally Posted by calc626 View Post
    hmm that's what i've been trying but have not been getting the right answer somehow. is the integral from 0 to 2pi?
    Yes. If you show us some of your details maybe we can help.
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