Find the Jacobian of the transformation.

x = 4u + v,y = 6u v

Answer all questions carefully, showing all work on a separate paper to receive full credit. 1. Compute the integral: a. with R the parallelogram enclosed by the lines 2x-3y = 0, 2x-3y = 2, 5x +y = 1 and 5x +y = 3. b. Il, ads with R the region bounded by the ellipse 9x2 + 4y? = 36. C. with R the rectangle enclosed by x - y = 0, x - y = 2, I +y = 0 and x+y=3. 2. Find the Jacobian of the transformation: a. x =u+ww, y =v+ wu, z =w+ uv. b. x = peg, y = gep. 3. Compute the integral: a. fo ydx + zdy + zdz, where C consists of Ci, the line segment from (1, -1, 1) to (2, 0, 4) followed by C2, the line segment from (2, 0, 4) to (3, 1, 2). b. Jc yds where C is the curve x = t2, y = 2t, 0