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Math Help - Green's Therorem...

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    Green's Therorem...

    Let C be the positively oriented square with vertices , , , . Use Green's Theorem to evaluate the line integral .
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by iwonder View Post
    Let C be the positively oriented square with vertices , , , . Use Green's Theorem to evaluate the line integral .

    Note that f\left(x,y\right)=7y^2x and f\left(x,y\right)=6x^2y

    Thus, \frac{\partial f}{\partial y}=14xy and \frac{\partial g}{\partial x}=12xy

    Also note that the region R is bounded by the lines x=0,~x=2,~y=0,~y=2

    Thus, by Green's Theorem,

    \oint_C7y^2x\,dx+6x^2y\,dy=-2\int_0^2\int_0^2xy\,dx\,dy

    Can you take it from here?
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