Evaluate the integral double integral _Re⁽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.