To evaluate the following integrals carry out these steps.

a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables.

b. Find the limits of integration for the new integral with respect to u and v.

c. Compute the Jacobian.

d. Change variables and evaluate the new integral.

xy dA, where R = {(x, y): 0 x 2, x y x +4}; R use x = 2u, y = 4v + 2u.