. Let h(x, y) = y x 2 , and let F(x, y) = h(x, y).

(a) Calculate F(x, y). Then plot F(x, y) as a vector field in the rectangle [0, 3] [0, 3]; draw arrows at all points with integer coordinates.

(b) Plot the level curves h(x, y) = k for k = 1, 0 and 1. What relation is there between these level curves and the vector field drawn in part (a)?

(c) Let C be the curve y = x 2 from (0, 0) to (1, 1). What would you expect the value of R C F dr to be? Why? Check by calculating the integral.