[See Solution] Derive the reduction formula given. Throughout, n denotes a positive integer with an appropriate side condition (such as n ≥qq 1 or n ≥qq 2).


Question: Derive the reduction formula given. Throughout, n denotes a positive integer with an appropriate side condition (such as \(n \geqq 1\) or \(n \geqq 2\) ).

\(\int \sin ^{n} x d x=-\frac{\sin ^{n-1} x \cos x}{n}+\frac{n-1}{n} \int \sin ^{n-2} x d x\)

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