Chapter 6.3, Problem 20ES

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

The Riemann sum approximation

$V\approx {\displaystyle \underset{k=1}{\overset{n}{\sum }}2\pi x_k^{*}f\left(x_k^{*}\right)\Delta x_k}\left(\text{where }{x}_k^{*}=\frac{x_k+x_{k-1}}{2}\right)$

for the volume of a solid of revolution is exact when $f$ is a constant function.