Answer
$$
\int_{1 / 2}^{1 / \sqrt{2}} \frac{4}{\sqrt{1-x^{2}}} d x =\frac{\pi}{3}
$$
Work Step by Step
$$
\begin{aligned}
\int_{1 / 2}^{1 / \sqrt{2}} \frac{4}{\sqrt{1-x^{2}}} d x &=[4 \arcsin x]_{1 / 2}^{1 / \sqrt{2}} \\
&=4\left(\frac{\pi}{4}-\frac{\pi}{6}\right) \\
&=4\left(\frac{\pi}{12}\right) \\
&=\frac{\pi}{3}
\end{aligned}
$$