Find the flux of F(x, y, z) = x, -z, y across the part of the sphere x2 + y2 + z2 = 4 in the first octant with orientation towards the origin. EXTRA CREDIT Evaluate int intS F · dS where F(x, y, z) = xy, yz, zx and S is the part of the paraboloid z = 4 - x2 - y2 that lies above the square 0 le x le 1, 0 le y le 1 with upward orientation.
