Chapter 8.2, Problem 33E

To determine

To prove:

The arc length of $y=f\left(x\right)$ over $\left[a,b\right]$ is at most $\sqrt{2}\left(b-a\right)$ if $0\le f^{\text{'}}\left(x\right)\le 1$ for all $x$. Also, the arc length of $f\left(x\right)=x$ is $\sqrt{2}\left(b-a\right)$.