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    Green's Theorem Used to Evaluate Integrals

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    Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

    Below, 'S' represents the integral sign.

    1) S_c xy dx + y^5 dy

    C is the triangle with verticies (0,0), (2,0) and (2,1).

    2) S_c (y + e^sqrt(x) )dx + (2x + cos(y^2) ) dy

    C is bounded by the region enclosed by parabolas y = x^2 and x = y2

    3) S_c x^2y dx - 3y^2 dy

    C is the circle x^2 + y^2 + 1

    4) S_c (x^3 - y^3) dx + (x^3 + y^3) dy

    C is the boundary of the region between circles x^2 + y^2 = 1 and x^2 + y^2 = 9.

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    Solution Summary

    The solution provides examples of using Green's theorem to evaluate line integrals in an attachment.