Category:Reduction Formula for Integral of Power of Sine

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


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

Let:

$I_n := \ds \int \sin^n x \rd x$

Then:

$I_n = \dfrac {n - 1} n I_{n - 2} - \dfrac {\sin^{n - 1} x \cos x} n$

is a reduction formula for $\ds \int \sin^n x \rd x$.