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Math Help - Green's theorem question?

  1. #1
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    Green's theorem question?

    The question
    Suppose R is a closed region in the plane bounded by a closed non-self-intersecting, piecewise smooth plane curve \tau. Prove that the area of R is given by

    \frac{1}{2}\oint_{\tau}{x \ dy - y \ dx}

    I'm unsure of how to solve this. Could someone guide me? Thanks.
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  2. #2
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    Quote Originally Posted by Glitch View Post
    The question
    Suppose R is a closed region in the plane bounded by a closed non-self-intersecting, piecewise smooth plane curve \tau. Prove that the area of R is given by

    \frac{1}{2}\oint_{\tau}{x \ dy - y \ dx}

    I'm unsure of how to solve this. Could someone guide me? Thanks.
    Just apply Green's theorem

     \frac{1}{2}\oint_{\tau}{x \ dy - y \ dx} =\frac{1}{2} \iint_{D} 1+1 dA=\iint_D dA
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  3. #3
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    Thanks, I didn't realise it was that simple.
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