Solving the surface Integral Using Gauss Divergence Theorem.

Question

Evaluate $\int Fnds$ over the entire surface of the region bounded above $xy$ plane bounded by the cone $z^2 = x^2 + y^2$ and the plane $z =4$ If $F = \hat{i} +\hat{j} - 3\hat{k}$ then Find $\int Fnds$

My question Is can I use Gauss Divergence theorem here ?

Because If I use Gauss Divergence then $\nabla.F =0$ hence Surface Integral Must be $0$.

Is this correct way to solve this ?

Can anyone please Explain?

Answer 1

Yes you are right, since we are asked to find the flux through a closed surface and $\nabla\cdot F =0$, the total flux is equal to zero.

Refer also to the related

• Why doesn't Gauss divergence work for this surface?