Chapter 15.6, Problem 1QCE

In these exercises, $\text{F(}x,y,z)$ denotes a vector field defined on a surface $\sigma$ oriented by a unit normal vector field $\text{n}(x,y,z),\text{and}\Phi$ denotes the flux of $\text{F}$ across $\sigma .$

(a) $\Phi$ is the value of the surface integral $\_\_\_\_\_.$

(b) If $\sigma$ is the unit sphere and n is the outward unit normal, then the flux of

$\text{F(}x,y,z)=x\text{i}+y\text{j}+z\text{k}$

across $\sigma \text{is}\Phi =\_\_\_\_\_\_$ .