Chapter 14.4, Problem 5QCE

Suppose $\sigma$ is a parametric surface with vector equation

$\text{r}\left(u,v\right)=x\left(u,v\right)\text{i}+\left(u,v\right)\text{j}+\text{z}\left(u,v\right)\text{k}$

If $\sigma$ has no self-intersections and $\sigma$ is smooth on a region R in the $uv\text{-plane},$ then the surface area of $\sigma$ is given by

$S={\displaystyle \underset{R}{\iint }\text{\_\_\_\_\_\_}dA}$