since and is a circle of radius 4.

By symmetry the only non-zero contribution of the flux of F through S is through the top of the cylinder ...... (You can check this - using cylindrical coordinates for the flux through the curved part of the cylinder is probably easiest but it can be done using cartesian coordinates too). Note that [tex]\vec{dS} = k dx dy on the ends of the cylinder.

Then the flux integral becomes .