Chapter 6.5, Problem 19ES

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

The approximation

$S\approx {\displaystyle \underset{k=1}{\overset{n}{\sum }}2\pi f}\left(x_k^{**}\right)\sqrt{1+{\left[f^{\prime }\left(x_k^{*}\right)\right]}^2}\Delta x_k$

for surface area is exact if $f$ is a positive-valued constant function.