(887, #23) Evaluate

where R is given by the inequality |x|+ |y| <= 1.

Solution: The four lines that satisfy the equation |x| + |y| = 1 form a diamond:

To contine, set u = x + y (so u = -1..1) and v = x -y (so v = -1..1). Next

Finally, since the jacobian is equal to -1/2,