I have to compute $\iint F \cdot \hat{N}dS$ of the half sphere $z^2+x^2+y^2=1$ and $z>0$ with $F=(-y,x,x^2+z)$.
I computed the flux by closing the surface with $x^2+y^2=1$ and got an answer $\frac{11 \pi}{12}$ which is correct. My question is. Could I instead use Stokes theorem? I know I can try, but if the answer is yes, then i will give it a try!
Thanks.