Lời giải

\( I = \frac{1}{a} \int_0^{\frac{a}{2}} \frac{1}{\sqrt{1 - \left(\frac{x}{a}\right)^2}} \, dx \)

Đặt \( \frac{x}{a} = \sin t \Rightarrow x = a \sin t \Rightarrow dx = a \cos t \, dt \)  

\( \begin{cases}
x = 0 \Rightarrow t = 0\\
x = \frac{a}{2} \Rightarrow t = \frac{\pi}{6}
\end{cases} \)

\( I = \frac{1}{a} \int_0^{\frac{\pi}{6}} \frac{1}{\sqrt{1 - \sin^2 t}} a \cos t \, dt \)

   \( = \int_0^{\frac{\pi}{6}} dt = t \Big|_0^{\frac{\pi}{6}} = \frac{\pi}{6} \)