Question

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

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

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