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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.

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  • $\begingroup$ I can't see why wouldn't you be able to use the divergence theorem... $\endgroup$ – DonAntonio Jan 10 at 13:11
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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 $0$.

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