Associated Topics || Dr. Math Home || Search Dr. Math

### Integration of Trigonometric Functions

```
Date: 05/28/99 at 09:14:00
From: Corenne
Subject: Integration in trigonometry

I am having problems with the following question:

Integrate sin(x)sin(2x).dx

I have tried integration by parts but it has not seemed to work.

u  = sin(x)
u' = -cos(x)
v' = sin(2x)
v  = 0.5cos(2x)

0.5sin(x)cos(2x)-(integral of)[-0.5cos(x)cos(2x).dx]

Thank you,

Corenne
```

```
Date: 05/28/99 at 10:17:50
From: Doctor Wilkinson
Subject: Re: Integration in trigonometry

Hi, Corenne. Integration by parts is a useful tool, but it's not a
magic wand. A good question to ask is "what's the main problem here"?

I'd say the main problem is that you have both sin(x) and sin(2x) and
they don't mix well. Fortunately, we have a formula for sin(2x) in
terms of sin(x) and cos(x). When you do integration involving trig
functions, you often need to apply trigonometry and not just calculus.
Writing

sin(2x) = 2sin(x)cos(x)   gives you the integral of

2sin^2(x) cos(x) dx

and now things are looking good, since cos(x) is the derivative of
sin(x).

- Doctor Wilkinson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus
High School Trigonometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search