6. (20 pts) Consider the vector field F = 3x2i + j + 2z In yk. (a) Use the component test to show that F is conservative on the region R = {(x, y, z) : y > 0}. (b) Find the function f(x, y, z) that satisfies F = Vf. (c) Compute Sc3x2 dx + 4 dy + 2zlny dz where C' is the circle x2 + 22 = 9 lying in the plane y = 5