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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+