Chapter 11: Parametric Equations and Polar Coordinates - Practice Exercises - Page 688: 14

$L \approx 7.634$

Here, we have $L=\int_{m}^{n}\sqrt{1+(\dfrac{dy}{dx})^2dy}=\int_{1}^{8} \sqrt{1+\dfrac{4}{9x^{(2/3)}}} dx$ This gives: $L=\int_{1}^{8} (x^{(-1/3)})\sqrt{(9x^{2/3}+4)}dx$ Therefore, $L=(\dfrac{1}{27})[40^{(3/2)}-13^{(3/2)}] \approx 7.634$