Green’s Theorem Used to Evaluate Integrals

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

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