The surface in is given by .
(a) Show that the vector field
is tangent to the surface everywhere.
(b) Show that the surface integral is a constant independent of for any surface which is a subset of , and determine this constant.
(c) The volume in is bounded by the surface and by the cylinder . Sketch and compute the volume integral
directly by integrating over .
(d) Use the Divergence Theorem to verify the result you obtained in part (b) for the integral , where is the portion of lying in .