Reduction Formula for Integral of Power of Cosine/Mistake

Source Work

2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.):

Appendix $8$: Integrals

Reduction Formulae

Mistake

For $I_n = \int \cos^n x \rd x$, where $n \ge 2$, then

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

Correction

The correct expression is:

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

Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $8$: Integrals: Reduction Formulae