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Math Help - Green's Theorem Question

  1. #1
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    Green's Theorem Question

    I'm trying to evaluate the line integral F(x,y)=\left ({\arctan y,\frac{-xy^{2}}{1+y^{2}}} \right ) around the curve 4x^{2}+9y^{2}=36

    Does anybody else get -6Pi?
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  2. #2
    Senior Member roninpro's Avatar
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    I just punched the integral into Mathematica and also received -6\pi.
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  3. #3
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    By Green's theorem

    \oint \limits_C Pdx + Qdy = \iint \limits_R Q_x - P_y dA

    which for your particular vector field gives

     \iint \limits_R -1 dA and the area of the ellipse is  6 \pi, hence your answer of - 6 \pi.
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