Chapter 15.6, Problem 20ES

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

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

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

$\begin{array}{l}\text{r}(u,v)=2\sin u\cos v\text{i}+\text{2}\sin u\sin v\text{j}+\text{2cos}u\text{k}\\ \text{with}0\le u\le \pi /3,0\le v\le 2\pi .\end{array}$