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    Green's Theorem and Line Integrals

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    Let gamma1 be given by (x,y)=(cos t , sin t), 0<t<pi/2 and gamma2 be given by (x,y) = (1-u,u) 0<u<1

    Integral of fdx + gdy over gamma1
    Integral of fdx + gdy over gamma2

    where f(x,y) = xy and g(x,y)=x+1

    see file for more details

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    Solution Preview

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    The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

    Green's theorem states that:

    Where D is the area enclosed by the curve .

    In our two case the curve is not ...

    Solution Summary

    The 8 pages solution shows in detailed manner all the steps needed to arrive at the answer.
    It utilizes both Green's theorem and direct integration to show the equivalency of both methods.