Chapter 10 - Practice Exercises - Page 593: 17

$10$

Since, $L=\int_{0}^{\pi/2}\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2}dt$ Thus, $L=\int_{0}^{\pi/2} 5\sqrt{2-2(\sin t\sin 5t+\cos t+\cos 5t)} dt$ or, $L=10\int_{0}^{\pi/2} \sqrt{\sin^2 2t} dt$ Thus, $L =\int_{0}^{\pi/2} 10 \sin 2t dt=10$