Calculate $\int_{\mathbb{S}^{n-1}}\|x-v\|dVol_{n-1}$ for $v\in\mathbb{R}^n,\|v\|<1$ by using the Divergance theorem.
I've thought of taking $F=\frac{x}{\|x\|}\|x-v\|$ but I think it will make the other integral hard aswel to solve and $N(x)=x$ normal to the unit sphere