$\displaystyle F = 3yi - 2yj + {z}^{2 }k$ S the hemisphere$\displaystyle {x}^{2 } + {y}^{2 } + {z}^{2 }=1$ $\displaystyle z\geqslant 0 $ So i ahve done $\displaystyle \nabla x F = 0i + 0j -3k$ Now my integral is $\displaystyle \iiint -3{r}^{ 2} sin\phi$ $\displaystyle dr d\phi d\theta $ where r is between 1 and 0, $\displaystyle d\phi $ is between $\displaystyle \frac{\pi }{ 2}$ and 0 and $\displaystyle d\theta$ is between $\displaystyle 2\pi$ and 0

But this isnt gettign me the right answer what have i done wrong