Use the divergence theorem to find the surface integral, that is, the flux integral of the vector field, by means of a triple integral. The vector field is given by F(x, y, z) = (xy + 2xz) i + (x^2 + y^2)j + (xy - z^2)k. The surface S consists of the northern hemisphere of the unit sphere z = sqrt(1 - x^2 - y^2) and the disk in the xy plane.