To evaluate the following integral, 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.
∬RxydA∬ R
xydA, where R is the square with vertices (0, 0), (1, 1), (2, 0), and (1, -1); use x=u+v, y=u-v.