3. For each of the following, compute Ic w.

(a) C is the polygonal path consisting of the line segment from (1,1) to (2,1)

followed by the line segment from (2,1) to (2,3), and w = y dx + x dy.

(b) C is the intersection of z = x2 + y2 and x2 + y2 + z2 = 1, oriented in the counterclockwise direction when viewed from high up the positive z axis, and w = dx + (x + y) dy + (x2 + xy + y2) dz.

(c) C is the boundary of the rectangle R = [a, b] x [c, d], oriented in the counterclockwise direction, and w = xy dx + (x + y) dy.

(d) C is the intersection of y = x and y = z2, 0 :::; Z :::; 1, oriented from left to right when viewed from far out the y axis, and w = yxdx + cosydy - dz.