Question

$\underset{0}{\overset{1/2}{\int }}\frac{1}{\sqrt{1-x^2}}dx$

Answer 1

$$\begin{gathered} \mathrm{Let}I={\int }_0^{\frac{1}{2}}\frac{1}{\sqrt{1-x^2}}\mathit{}\mathit{d}x.\mathrm{Then}, \\ I={\left[{\sin }^{-1}x\right]}_0^{\frac{1}{2}} \\ \Rightarrow I={\sin }^{-1}\frac{1}{2}-{\sin }^{-1}0 \\ \Rightarrow I=\frac{\mathrm{\pi }}{6}-0 \\ \Rightarrow I=\frac{\mathrm{\pi }}{6} \end{gathered}$$