فرمول والیس

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

${\displaystyle {\int }_0^1\sqrt{x-x^2}dx=\frac{(\frac{1}{2}!{)}^2}{2!}}$

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

${\displaystyle \underset{n\to \mathrm{\infty }}{lim}\frac{{\int }_0^{\frac{\mathrm{\Pi }}{2}}{\sin }^{n}xdx}{{\int }_0^{\frac{\mathrm{\Pi }}{2}}{\sin }^{n+1}xdx}=1}$

${\displaystyle {\int }_0^{\frac{\mathrm{\Pi }}{2}}{\sin }^{m}xdx=\frac{(m-1)!}{m!!}}$

${\displaystyle {\int }_0^{\frac{\mathrm{\Pi }}{2}}{\sin }^{m}xdx=\frac{(m-1)!}{m!!}\frac{\mathrm{\Pi }}{2}}$