Chapter 6.4, Problem 16ES

The curve segment $y=x^2$ from $x=1$ to $x=2$ may also be expressed as the graph of $x=\sqrt{y}$ from $y=1$ to $y=4$ . Set up two integrals that give the arc length of this curve segment, one by integrating with respect to $x$ , and the other by integrating with respect to $y$ . Demonstrate a substitution that verifies that these two integrals are equal.