Category:Reduction Formula for Definite Integral of Power of Sine

This category contains pages concerning Reduction Formula for Definite Integral of Power of Sine:

Let $n \in \Z_{> 0}$ be a positive integer.

Let $I_n$ be defined as:

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

Then $\sequence {I_n}$ is a decreasing sequence of real numbers which satisfies:

$n I_n = \paren {n - 1} I_{n - 2}$

Thus:

$I_n = \dfrac {n - 1} n I_{n - 2}$

is a reduction formula for $I_n$.