Let C be the circle of radius 2 about the origin traversed counterclockwise. Consider the line integral ?_C(x^2 + y^2)dx + (x^2 + x - y^2)dy. (a) (3 points) Is the vector field in the integral conservative? (b) (5 points) Use Green's theorem to write the line integral as a double integral. Don't forget to indicate the region for the double integral. (c) (5 points) Use polar coordinates to evaluate the double integral.
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