Answer
$\approx 7.634$
Work Step by Step
Since, $L=\int_{1}^{8}\sqrt{1+(\dfrac{dy}{dx})^2dy}$
Thus, $L=\int_{1}^{8} \sqrt{1+\dfrac{4}{9x^{2/3}}} dx=\int_{1}^{8} (x^{-1/3})\sqrt{(9x^{2/3}+4)}dx$
or, $L=(\dfrac{1}{27})[40^{3/2}-13^{3/2}]$
Thus, $L \approx 7.634$
