Mathematics · supplementary
Beta-type evaluation of mixed powers for JEE
Evaluation of definite integrals
Formula
\[\int_0^{\pi/2}\sin^m x\cos^n x\,dx=\frac{(m-1)(m-3)\cdots}{(m+n)(m+n-2)\cdots}\times\begin{cases}\frac{\pi}{2},& m,n\text{ both even}\\1,& \text{otherwise in standard Wallis form}\end{cases}\]
Variables: \(m,n\) are nonnegative integers.
Conditions: Interpret products until reaching 1 or 2 appropriately.
JEE evaluation of mixed power trigonometric integrals.