I have $F=xyi-y^2j+zk$
Over surface $z=0$, $s \le1 $, $x^2+y^2 \le s$
My approach to calculate $ \iint F.ds$ was the outward normal is $k$ the dot product of this with F gives z so integral becomes $\iint z.ds$ however z=0 on this disk so the surface integral is zero? is this correct?