Verify my calculation of the surface integral without divergence theorem

46 Views Asked by At

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?