Let S be the portion of the sphere: x^2 + y^2 + z^2 = 9 which lies between the planes: z = 1 and z = 2 , oriented by the unit normal vector N which points away from the origin. Evaluate the flux integral:
, where F is the vector field given by: F (x, y, z) = ( x + y z^(3) )i + x z^(3)j - z k