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    Green's Theorem : Evaluating a Line Integral

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    Use Green's Theorem to evaluate the line integral Sc xy dx +x^2y^3 dy where C is the triangle with vertices (0,0), (2,0) and (2,2).

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    I = integration (along C) [x*y*dx + x^2*y^3*dy]

    By Green's theorem,
    integration(along C)[f1*dx + f2*dy]
    = integration (over region E) [ del(f2)/del(x) - del(f1)/del(y)]dx*dy

    Here,
    f1 = x*y => del(f1)/del(y) = x,
    and,
    f2 = x^2*y^3 => ...

    Solution Summary

    Green's Theorem is used to evlauate a line integral. The solution is well-explained.

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