Reduction Formula

Derive the reduction formula below:

Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Example, p. 233)

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

Sources:

Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Example 4, p. 366-367)

Silverman, R.A. (1985). Calculus with Analytic Geometry. Englewood Cliffs, NJ: Prentice-Hall. (Example 1, p. 379)

Swokowski, E.W. (1984). Calculus with Analytic Geometry (3rd ed.). Boston, MA: Prindle, Weber & Schmidt. (Example 6, p. 406)

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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