the problem: evaluate the following integral by making appropriate change of variables. double integral, over region R, of xy dA R is bounded by lines: 2x - y = 1 2x - y = -3 3x + y = 1 3x + y = -2 my attempt: let 2x - y = u, and let 3x + y = v then the new region in (u,v) coordinates is bounded by the following lines: u = 1 u = -3 v = 1 v = -3 I calculated the Jacobian of u and v, with respect to x and y, and got 5. The area in (u,v) coordinates also looks like it could be 5 times the area in (x,y) coordinates. Solving for x and y, I get x = (u + v)/5, y = (2v - 3u)/5 Then I integrated [(-uv - 3u2 + 2v2)/125] du dv, where u is from -3 to 1, and v is from -2 t o 1. I got -102/125. The correct answer is -66/125. What am I doing wrong?