1. For each of the following, evaluate Ie F . T ds.

(a) C is the topological boundary of the two-dimensional region in the first quadrant bounded by x = 0, y = 0, and y = J4"=X2, oriented in the counterclockwise direction, and F(x, y) = (sin( Jx3 - x2), xy).

(b) C is the perimeter of the rectangle with vertices (0,0), (2,0), (0,3), (2,3), oriented in the counterclockwise direction, and F(x, y) = (eY , log(x + 1)).

(c) C = C1 U C2 , where C1 = 8B1 (0, 0) oriented in the counterclockwise direction, C2 = 8B2 (0, 0) oriented in the clockwise direction, and F(x, y) =

(f(x2 + y2), xy2), where f is a C1 function on [1,2].