We have $\mathbf{x}=\left(x_1,\cdots,x_n\right)\in\mathbb R^n$ and $\mathbf{v(x)=x}.$ How can we apply Gauss' divergence theorem to $\mathbf{v}$ over the unit ball $$B=\{ \mathbf{x}\in\mathbb R^n:\displaystyle\sum_{i=1}^{n}x_i^2\leq1\}$$.Thank you
MY TRY:Gauss' divergence theorem for multiple dimension is $$\int\cdots\int_{n\,\text{times}}\nabla\,\mathbf{F}\,dv=\int\cdots\int_{{n-1}\,\text{times}}\mathbf{F}\,\mathbf n\, ds$$.But I am unable to proceed further.
