Chapter 6.4, Problem 11ES

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

The approximation

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

for arc length is exact when $f$ is a linear function of $x$ .