Question

1 Consider the vector field F(x, y) = − xy, x2 . [6] a) Let C1 be the quarter circle from (0, 2) to (−2, 0). Evaluate Z C1 F · dr. (Hint: C1 can be parameterized by r(t) = h2 cos(t), 2 sin(t) ifor π/2 ≤ t ≤ π.)

6] b) Let C2 be the line segment from (0, 2) to (−2, 0). Evaluate Z C2 F · dr.

2] c) From your answers from a) and b) is it possible that F is a conservative field? If so find the potential function