Integrating Odd Powers of Sine and Cosine by Substitution

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
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.

 
Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed.
Privacy Policy »

Note: To run this Demonstration you need the free
Mathematica Player
or Mathematica 7+
Download or upgrade to Mathematica Player 7
I already have Mathematica Player or Mathematica 7+