How to calculate $\int_{0}^{\pi/3} \sqrt{\sec ^2 (x)} dx$? I'm trying to calculate the following integral:
$\int_{0}^{\pi/3} \sqrt{\sec^2 (x)} dx$
But I have no idea where to start. Can you give me some advice?

As on the integration interval, $\sec x>0$, we may simplify to
$$\int_0^\tfrac\pi3\sec x\,\mathrm dx=\int_0^\tfrac\pi3\frac{\mathrm dx}{\cos x}=\int_0^\tfrac\pi3\frac{\cos x\,\mathrm dx}{\cos^2 x}.$$
Can you continue?
