$3$\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}} $ }$

$3$\displaystyle{x=0}$ 　のとき　 $3$\displaystyle{t=0}$
$3$\displaystyle{x=a}$ 　のとき　 $3$\displaystyle{t=\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}}}$
また、 $3$\displaystyle{dx=a\cos tdt}$
　 $3$\displaystyle{\int _{0}^{a} \sqrt{ {a}^{2}- {x}^{2} }dx }$
$3$\displaystyle{=\int _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } \sqrt{ {a}^{2}- {a}^{2}{ \sin }^{2}t } }$ 　 $3$\displaystyle{a\cos tdt}$
$3$\displaystyle{=\int _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } a\sqrt{ 1- { \sin }^{2}t } }$ 　 $3$\displaystyle{a\cos tdt}$
$3$\displaystyle{=\int _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } a\sqrt{ { \cos }^{2}t } }$ 　 $3$\displaystyle{a\cos tdt}$
$3$\displaystyle{{}^\bullet\limits{ }_\bullet {}^\bullet 1- {\sin }^{2}t={\cos }^{2}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}}}$ 　より　 $3$\displaystyle{\sqrt{ { \cos }^{2}t }=\cos t}$
$3$\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{{}^\bullet\limits{ }_\bullet {}^\bullet }$ 半角の公式
$3$\displaystyle{={a}^{2} \[ \frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}}+\frac{\hspace{2}1\hspace{2}}{\hspace{2}4\hspace{2}}\sin 2t \] _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} }}$
$3$\displaystyle{{}^\bullet\limits{ }_\bullet {}^\bullet }$ 積分の公式基本編
$3$\displaystyle{=\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}}{a}^{2}}$

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