## anonymous 4 years ago What is the arclength from x=0 to x=9 of this curve: y=1/3 (√x)(x−3) I can get most of the way there, but I run into mechanical problems when I try to actually evaluate the integral

$Arc length = \int\limits_{0}^{9}\sqrt{1+f'(x)^{2}}dx$ $f'(x) = \frac{x-3}{6\sqrt{x}}+\frac{\sqrt{x}}{3} = \frac{x-1}{2\sqrt{x}}$ $\rightarrow \int\limits_{0}^{9}\frac{x+1}{2\sqrt{x}}dx$ $= \frac{1}{2}\int\limits_{0}^{9}(x^{1/2}+x^{-1/2})dx$ $=\frac{1}{3}x^{3/2}+x^{1/2} from 0->9$ $=12$