So I am given the following question:
On $\mathbb{R}^3\backslash \{\underline{0}\}$ consider the vector field \begin{align*} \underline{F}(x,y,z) = (0,\frac{-2yz}{r^4}, \frac{-1}{r^2}+ \frac{2y^2}{r^4}), \text{with } r = \sqrt{x^2+y^2+z^2} \end{align*} and the surface $\mathcal{S}$ given by $x^2+y^2+\frac{1}{4}z^2 = 1$, $z\geq0$. The surface normal points away from the origin. Evaluate $\iint\limits_{\mathcal{S}} (\underline{F}, \underline{n}) \ d\sigma$.
I am struggling to approach this question since the $0$ vector is not included in the domain. Do I have to make any special considerations that we would not do if we took the whole of $\mathbb{R}^3$? Any help/hints with the initial steps is appreciated.