\[
\int {\sqrt {a^2  - x^2 } dx}  = \left[ \begin{array}{l}
 x = a\sin t \\ 
 dx = a\cos tdt \\ 
 \end{array} \right] = \int {\sqrt {a^2  - a^2 \sin ^2 t} a\cos tdt}  = \int {a^2 \cos ^2 tdt}  = a^2 \int {\cos ^2 tdt}  = ...
\]