Answer
$\dfrac{32}{3}$
Work Step by Step
We know that the formula to calculate the arc length is defined as: $L=\int_m^n \sqrt {1+[f'(x)]^2} dx$
Re-write the equation as follows: $[f'(x)]^2=\dfrac{(y-1)^2}{4y}$
This implies that $L=\int_1^9 [1+\dfrac{(y-1)^2}{4y}] dx $
$L=(\dfrac{1}{2})[\int_1^9\dfrac{y}{y^{1/2}}+\int_1^9\dfrac{1}{y^{1/2}}] \\ \implies L= \dfrac{1}{2}[\dfrac{y^{(3/2)}}{(3/2)}+\dfrac{y^{(1/2)}}{(1/2)}]_1^9=\dfrac{32}{3}$
