LIST Next Problem (1 point) (a) Show that each of the vector fields F = yi + x j, G = _ -x * 2 + 1/2 x2+x2 j, and H = X y j are gradient vector /x2+y2 Vx2+12 fields on some domain (not necessarily the whole plane) by finding a potential function for each. For F, a potential function is f(x, y) = For G, a potential function is g(x, y) = For H, a potential function is h(x, y) = (b) Find the line integrals of F, G, H around the curve C given to be the unit circle in the xy-plane, centered at the origin, and traversed counterclockwise. JoF . dr= JcG . dr= SCH . dr= (c) For which of the three vector fields can Green's Theorem be used to calculate the line integral in part (b)? It may be used for ? (Be sure that you are able to explain why or why not.) Note: You can earn partial credit on this