## Quick Reference

Let *I*_{n} be some quantity that is dependent upon the integer *n*(≥0). It may be possible to establish some general formula, expressing *I*_{n} in terms of some of the quantities *I*_{n−1}, *I*_{n−2},…. Such a formula is a reduction formula and can be used to evaluate *I*_{n} for a particular value of *n*. The method is useful in integration. For example, if

*I*_{n} = *∫*_{0}^{π/2} sin^{n}*x**dx*,

it can be shown, by integration by parts, that *I*_{n}=(*n*−1)/*n*)*I*_{n−2} (*n*≥2). It is easy to see that *I*_{0}=*π*/2, and then the reduction formula can be used, for example, to find that

*Subjects:*
Mathematics.

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