1)

$\displaystyle S: x^2 + 4y^2 = 4$, $\displaystyle 0 \leq z \leq 1$. Calculate the flux of the vector field $\displaystyle \overline{A}(x,y,z) = \left(\frac{-6x}{x^2+y^2},\frac{-6y}{x^2+y^2}, z+1\right)$ out through the z-axis.

2)

$\displaystyle S: z=1 - \sqrt{x^2 +y^2}$, $\displaystyle 0 \leq z \leq \frac{1}{2}$ and the vector field $\displaystyle \overline{A}(x,y,z)=\frac{1}{\sqrt{x^2+y^2}}(x, 1, 0)$ are given. Calculate the flux of $\displaystyle \overline{A}$ through S in the direction $\displaystyle N \cdot ze_z > 0$ (the z part of the normal is > 0)