Gauss Divergence Theorem

Gauss Divergence Theorem:

Statement: If V is the volume bounded by a surface S and is continuously differentiable vector function then.


Where n^ is the positive unit vector outward drawn normal to S.

Example: Using the divergence theorem, evaluate and S is the surface of the solid cut off by the plane x y z = a from the first octant.

Solution: Now


Hence, By divergence theorem, we have