Integrating Odd Powers of Sine and Cosine by Substitution

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This Demonstration shows the first two steps in how to put an odd power of a sine into a form suitable for integration. Suppose the expression is . (1) split off one sine to get (2) use to express in terms of (3) substitute , because , which absorbs the split-off sine (4) expand the polynomial in (unless ) (5) integrate the resulting polynomial in terms of (6) substitute back

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The same technique applies to odd powers of cosines. This technique does not work for even powers of sine or cosine; in that case use a reduction formula instead.

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Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA


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