1. (8 pts) Evaluate the integral |(3x + 2y)2 /2y - x da over the region R bounded by A(0, 0), B(-2,3), C(2,5), D(4,2). Hint: Make sure the determinant is positive! OR xy 2. (8 pts) Evaluate the integral JR 1 + x2y2 z dA over the region R bounded by xy = 1, xy = 4, x = 1 and x = 4. Hint: Justify the choice x = u, y = v/u. 3. (6 pts each) Compute the following line integrals. (a) || (x2 + y2 + z)ds where C is the curve r(t) = (sint, cos t, t), Osts 37/4. dr where F(x, y) = (x + y,x - y) and C is the ellipse 4. (6 pts) Use the fundamental Theorem of Line Integrals to compute (, (2xy dx + (x2 + y2) dy where C is the curve y = x4 - x3, 0
