# Evaluate $\int \vec{F}.ndS$ where $S$ is the entire surface of the solid formed by?

Evaluate $$\int \vec{F}.ndS$$ where $$S$$ is the entire surface of the solid formed by $$x^2+y^2=a^2, z=x+1, z=0$$ and $$n$$ is the outward drawn unit normal and the vector function $$\vec{F}=\langle2x,-3y,z\rangle$$

My question is, can I directly apply the divergence theorem in this? Using the divergence theorem, since divergence of F is zero, we are getting zero.

• I can't see why wouldn't you be able to use the divergence theorem... – DonAntonio Jan 10 at 13:11

You can apply the divergence theorem here. $$\nabla\cdot\vec F=\Big(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z}\Big)\cdot\big(2x,-3y,z\big)=2-3+1=0$$giving the answer $$0$$.