Verify Green’s Theorem by using a computer algebra system to evaluate both the line integral and the double integral.

P(x, y) = y²e^x, Q(x, y) = x²e^y, C consists of the line segment from (–1, 1) to (1, 1) followed by the arc of the parabola y = 2 – x² from (1, 1) to (–1, 1)

Data from Green's Theorem

Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If P and Q have continuous partial derivatives on an open region that contains D, then

If | Pdx + Q dy = D dA