Gauss Divergence Theorem Calculation help I am having trouble getting my head around what exactly is required in this problem. Let $S$ be an arbitrary piecewise smooth, orientable, closed surface enclosing a region $\mathbb{R}^3$. Calculate $$\iint\limits_s a \cdot n\:\text{d}S$$ Where $n$ is an outwardly directed unit normal vector to $S$, and $a$ is a constant vector field in $\mathbb{R}^3$. I very much appreciate any help :)

By Gauss-Ostrogradski we have: $$ \iint\limits_S a\:n\:\text{d}S=\iiint\limits_V \text{div}(a)\:\text{d}V=0, $$ because $$ \text{div}(a) = \frac{\partial a_x}{\partial x}+\frac{\partial a_y}{\partial y}+\frac{\partial a_z}{\partial z}=0. $$