I was asked to use the divergence theorem to evaluate $\int_S \vec F\cdot d\vec S$, where $S$ is the top half of the sphere $x^2+y^2+z^1=1$ oriented upwards and $\vec F=1z^2x\vec i+(\frac 13y^3+\tan(z))\vec j+(1x^2z+2y^2)\vec k$.
For my divergence I got $div\vec F=z^2+y^2+x^2$. I then parameterized and solved using spherical coordinates to get $$\int_S \vec F\cdot d\vec S=\iiint_E \rho^2(\rho^2\sin(\phi))dV=\int_0^{2\pi}\int_0^{\pi/2}\int_0^1 \rho^4\sin\phi d\rho d\phi d\theta=\frac{2\pi}5$$
However, this answer apparently isn't correct. I've double checked that I'm evaluating the integral correctly, so I'm assuming that there's an issue with how I'm setting up my integral. I've been trying to think of other ways to set up this integral for over an hour, but I've come up with nothing. Any help would be appreciated.