I have a Stokes question.
$C$ is a curve created by intersection of a cylinder $x^2+y^2=9$ and a plane $z=1+y-2x$. The curve is clockwise when viewed from the positive $z$-axis. The vector function is $$F(x,y,z)=\langle 4z,-2y,2y\rangle.$$
I have done this a few times and keep getting $0$. The curl $F$ is not equal to zero, so this is a non-conservative vector field.
I am wondering how I can have flux $= 0$ here, when the vector field is non-conservative? Perhaps I did something wrong?