$3$\displaystyle{x=a\cos t}$ 　　 $3$\displaystyle{ $ 0\leq t\leq {\pi} $ }$

$3$\displaystyle{x=0}$ 　のとき　 $3$\displaystyle{t=\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}}}$
$3$\displaystyle{x=a}$ 　のとき　 $3$\displaystyle{t=0}$
また、 $3$\displaystyle{dx=- a\sin tdt}$
　 $3$\displaystyle{\int _{0}^{a} \sqrt{ {a}^{2}- {x}^{2} }dx }$
$3$\displaystyle{=\displaystyle{ \int _{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} }^{0} \sqrt{ {a}^{2}- {a}^{2}{ \cos }^{2}t } }}$ 　 $3$\displaystyle{ $ - a\sin t $ dt}$
$3$\displaystyle{=\int _{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} }^{0} a\sqrt{ 1- { \cos }^{2}t } }$ 　 $3$\displaystyle{ $ - a\sin t $ dt}$
$3$\displaystyle{=\int _{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} }^{0} a\sqrt{ { \sin }^{2}t } }$ 　 $3$\displaystyle{ $ - a\sin t $ dt}$
$3$\displaystyle{{}^\bullet\limits{ }_\bullet {}^\bullet 1- {\cos }^{2}t={\sin }^{2}t}$ 　⇒
$3$\displaystyle{0\leq t\leq {\pi}}$ 　より　　 $3$\displaystyle{\sqrt{ { \sin }^{2}t }=\sin t}$
$3$\displaystyle{=- {a}^{2}\int _{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} }^{0} { \sin }^{2}t dt}$
定積分の公式　より
$3$\displaystyle{={a}^{2}\int _{0}^{ \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} } { \sin }^{2}t dt}$
$3$\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} \[ \frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}}t- \frac{\hspace{2}1\hspace{2}}{\hspace{2}4\hspace{2}}\sin 2t \] _{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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