\[S\]
is any surface enclosing a volume \[V\]
and \[\mathbf{F} = ax \mathbf{i} + by \mathbf{j} + cz \mathbf{k}\]
then \[\mathbf{\nabla} \cdot \mathbf{F} =a+b+c\]
Applying the divergence the orem<:
\[\begin{equation} \begin{aligned} \int \int_S \mathbf{F} \cdot \mathbf{n} dS &= \int \int \int_V \mathbf{\nabla} \cdot \mathbf{F} dV \\ &= \int \int \int_V (a+b+c) dV \\ &= (a+b+c) \int \int \int dV \\ &= (a+b+c) V \end{aligned} \end{equation}\]