Reduction Formula

Derive the reduction formula below:

    \[\displaystyle \int \sin^n {ax} \cdot \cos^m {ax} \,\mathrm{d}x =\\ - \frac {\sin^{n-1} {ax} \cdot \cos^{m+1} {ax} }{ a (m+n) } + \frac{n-1}{m+n} \int \sin^{n-2} {ax} \cdot \cos^m {ax} \,\mathrm{d}x\]

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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