Math Help - Surface Integral

I thought about doing the divergence theorem, but then quickly noticed nothign differentiated

and S is the surface cut from the cylinder . by the planes

F is solenoidal and applying the divergence theorem to that surface isn't a problem, so the outward flux is zero.

Originally Posted by Mondreus

F is solenoidal and applying the divergence theorem to that surface isn't a problem, so the outward flux is zero.

So then the answer will be 0, because your integral will now be multiplied by 0?