Let D be the region in the xy-plane bounded by y = x and y = x², and C be the associated boundary curve with counter clockwise orientation. (a) Find the intersections of y = x and y = x² and thus sketch the region D. (b) Compute the line integral ${(xy + y²) dx + x² dy} directly by parametrising the path C. (c) Use Green's Theorem in the plane to compute the above line integral by evaluating a double integral.

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