First, here's the problem:

A curve is given by $\displaystyle y=(9-x^\frac{2}{3})^\frac{3}{2} ; 1\leq y\leq 8 $. Find the exact length of the curve analytically by antidifferentiation.

First I found the derivative of $\displaystyle y=(9-x^\frac{2}{3})^\frac{3}{2}$, then I tried to integrate it from 1 to 8. The answer I got is 10.6712.

Can anyone confirm this answer?