Calculate the flux of $\displaystyle F(x,y,z)=(\frac{x}{x^2+y^2},\frac{y}{x^2+y^2},z)$ through the surface $\displaystyle z=\sqrt{x^2+y^2}, \ \ \ 1\leq z \leq 2$.
The normal has a positive z-component.
**I do not know how to close the surface really.