Chapter 11: Parametric Equations and Polar Coordinates - Practice Exercises - Page 688: 17

$10$

Here, we have $L=\int_{0}^{\pi/2}\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2}dt$ This gives: $L=\int_{0}^{\pi/2} 5\sqrt{2-2((\sin t)(\sin 5t)+(\cos t)+(\cos 5t))} dt$ or, $L=(10) \int_{0}^{\pi/2} \sqrt{\sin^2 2t} dt$ Hence, $L =(10) \int_{0}^{\pi/2} \sin 2t dt=10$