Reduction Formula

Derive the reduction formula below:

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

Sources:

Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Exercise 17e: Question 6, p. 235)

Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Exercise 6.7, Question 5, p. 368)

Silverman, R.A. (1985). Calculus with Analytic Geometry. Englewood Cliffs, NJ: Prentice-Hall. (Example 2, p. 379)

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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