Answer
\[ = \frac{\pi }{6}\]
Work Step by Step
\[\begin{gathered}
\int_0^1 {\frac{{dx}}{{\sqrt {4 - {x^2}} }}} \hfill \\
\hfill \\
rewrite\,\,the\,\,deno\min ator \hfill \\
\hfill \\
= \int_0^1 {\frac{{dx}}{{\sqrt {\,{{\left( 2 \right)}^2} - {x^2}} }}} \hfill \\
\hfill \\
use\,\,\,\,the\,\,formula\,\int_{}^{} {\frac{{du}}{{\sqrt {{a^2} - {u^2}} }}} \, = \,\,\arcsin \,\left( {\frac{u}{a}} \right) + C \hfill \\
\hfill \\
= \,\,\left[ {\arcsin \,\left( {\frac{x}{2}} \right)} \right]_0^1 \hfill \\
\hfill \\
Fundamental\,\,theorem \hfill \\
\hfill \\
= \arcsin \,\left( {\frac{1}{2}} \right) - \arcsin \,\left( 0 \right) \hfill \\
\hfill \\
= \frac{\pi }{6} \hfill \\
\end{gathered} \]
