Chapter 15.6, Problem 17ES

Find the flux of the vector field F across $\sigma$ in the direction of positive orientation.

$\text{F(}x,y,z)=x\text{i}+y\text{j}+\text{k;}\sigma$ is the portion of the paraboloid

$\begin{array}{l}\text{r}(u,v)=u\cos v\text{i}+u\sin v\text{j+}(1-u^2)\text{k}\\ \text{with}1\le u\le 2,0\le v\le 2\pi .\end{array}$