فرمول والیس

${\displaystyle y={\sqrt {x-x^{2}}}}$

${\displaystyle \int _{0}^{1}{\sqrt {x-x^{2}}}{dx}={\frac {({\frac {1}{2}}!)^{2}}{2!}}}$

${\displaystyle {\frac {2}{\Pi }}={\frac {1.3.3.5.5.7...}{2.2.4.4.6.6...}}}$

${\displaystyle \lim _{n\to \infty }{\frac {\int _{0}^{\frac {\Pi }{2}}\,\sin ^{n}x{dx}}{\int _{0}^{\frac {\Pi }{2}}\,\sin ^{n+1}x{dx}}}=1}$

${\displaystyle \int _{0}^{\frac {\Pi }{2}}\,\sin ^{m}x{dx}={\frac {(m-1)!}{m!!}}}$

${\displaystyle \int _{0}^{\frac {\Pi }{2}}\,\sin ^{m}x{dx}={\frac {(m-1)!}{m!!}}{\frac {\Pi }{2}}}$