A Divergence Integral Proportional to Volume

If  
\[S\]
  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<:>
\[\begin{equation} \begin{aligned} \int \int_S \mathbf{F} \cdot \mathbf{n} dS &= \int \int \int_V \mathbf{\nabla} \cdot \mathbf{F} dV \\ &= \int \int \int_V (a+b+c) dV \\ &= (a+b+c) \int \int \int dV \\ &= (a+b+c) V \end{aligned} \end{equation}\]