I am lost with that problem, and I cannot continue.

The problem asks to calculate that:

$ $ \oint_S\ F.dS$ $ Being:

$ $ F = (x^2, y^2, (z^2-1))$ $

and S is defined by these Cylindrical coordenates: $ $ r = 2; 0<z<2; 0\leqΦ\leq2π$ $

I converted F to cylindrical coordenates to have both in the same system. I figured out for cylindrical system: $ $ dS = (r.dΦ.dz)\hat ar + (dr.dz)\hat aΦ + (r.dr.dΦ) \hat az$ $

But is that the best way to do that with surface integrals? Seems, that integral gives a lot of job. Plese help me.