Category:Definite Integral from 0 to Half Pi of Even Power of Sine x

$\ds \int_0^{\frac \pi 2} \sin^{2 n} x \rd x$

$=$

$\ds \dfrac {\paren {2 n}!} {\paren {2^n n!}^2} \dfrac \pi 2$

$\ds $

$=$

$\ds \dfrac {1 \cdot 3 \cdot 5 \cdots \paren {2 n - 1} } {2 \cdot 4 \cdot 6 \cdots 2 n} \dfrac \pi 2$

for $n \in \Z_{>0}$.

Pages in category "Definite Integral from 0 to Half Pi of Even Power of Sine x"

The following 3 pages are in this category, out of 3 total.