Chapter 13.7, Problem 49PS

To determine

To prove: Green’s second identity using the divergence theorem, that is ${\displaystyle \underset{D}{\iiint }\left(f{\nabla }^{2}g-g{\nabla }^{2}f\right)dV}={\displaystyle \underset{S}{\iint }\left(f\frac{\partial g}{\partial n}-g\frac{\partial f}{\partial n}\right)dS}$ ; where $f$ and $g$ are scalar functionssuch that $\overrightarrow{F}=f\nabla g$ is continuously differentiable in the region $D$ , which is bounded by the closed surface $S$ .