$3$\displaystyle{\int _{0}^{a} \sqrt{ {a}^{2}- {x}^{2} } dx}$

$3$\displaystyle{ x=a\sin t }$ 　 $3$\displaystyle{ $ - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}}\leq t\leq \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} $ }$
とおいたとき
与式 $3$\displaystyle{={a}^{2}\int _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } \frac{\hspace{2} 1+\cos 2t \hspace{2}}{\hspace{2}2\hspace{2}} dt}$
⇒
$3$\displaystyle{x=a\cos t}$ 　 $3$\displaystyle{ $ 0\leq t\leq {\pi} $ }$ とおいたとき
与式 $3$\displaystyle{={a}^{2}\int _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } \frac{\hspace{2} 1- \cos 2t \hspace{2}}{\hspace{2}2\hspace{2}} dt}$
⇒