Answer
$\dfrac{32}{3}$
Work Step by Step
Formula to calculate the arc length is: $l=\int_p^q \sqrt {1+[f'(x)]^2} dy$
The given equation can be differentiated and re-written as: $[f'(x)]^2=\dfrac{(y-1)^2}{4y}$
Now, $l=\int_1^9 [1+\dfrac{(y-1)^2}{4y}] dx =\dfrac{1}{2}[\int_1^9\dfrac{y}{y^{1/2}}+\int_1^9\dfrac{1}{y^{1/2}}]$
Since, we know $\int x^n dx=\dfrac{x^{n+1}}{n+1}+C$
or,$ \dfrac{1}{2}[\dfrac{y^{3/2}}{3/2}+\dfrac{y^{1/2}}{1/2}]_1^9=\dfrac{32}{3}$
