4. (30pts) The following questions are on the flux of vector fields. (a) (15pts) Find JJ F . dS, where F(x, y, 2) = (x3 + e += )i+ (y) + In(1 + x?))j + (x3 + yo)k, and S is the sphere with center at the origin and radius 3 such that S is oriented outward. (b) (15pts) Let F(x, y, 2) = zarctan(y?)i + 2 In(a' + 1)j + c zk. Find the flux of F across the surface S, which is the part of r2 + y? + 2 = 2 that lies above the plane z = 1 and is oriented upward