Evaluate the integral ∫∫R e(x + y)/(x - y) dA, where R is the trapezoidal region with vertices (1, 0), (2, 0), (0, -2) and (0, -1).
a. Sketch the region R and choose an appropriate change of variables for the transformation to the region S in the uv-plane.
b. Calculate the Jacobian, determine the limits of integration, and evaluate the transformed integral.