Chapter 14.4, Problem 47ES

Determine whether the statement is true or false. Explain your answer.

If $f$ has continuous first partial derivatives in the interior of a region $R$ in the $xy\text{-plane},$ then the surface area of the surface $z=f\left(x,y\right)$ over $R$ is

${\displaystyle \underset{R}{\iint }\sqrt{{\left[f\left(x,y\right)\right]}^2+1}dA}$