# Integral (cos x)^2 dx

1. Apr 28, 2004

Do any one have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!

2. Apr 28, 2004

### mathman

cos2x+sin2x=1
cos2x-sin2x=cos2x
Therefore cos2x=(1+cos2x)/2

I'll let you finish.

3. Apr 28, 2004

Thank you. :) integral (cos x)^2 dx

Last edited by a moderator: Feb 17, 2008
4. Mar 3, 2008

### mussgo

dont you have to use half angle identities to get integral of cos^2 ?

5. Mar 3, 2008

### HallsofIvy

No, double angle formulas as mathman said.

6. Mar 5, 2008

### jacobrhcp

an easy way to remember the solution to this common integral, when integrating over a whole period:

cos^2 x + sin ^2 x =1
$$\int cos^2 x = \int sin^2 x$$
, at least when you integrate over a whole period

$$\int cos^2 x + \int sin^2 x =$$ length of a period

so the integral gives length of a period divided by 2

7. Mar 5, 2008

### awvvu

Why does this thread have over 16,000 views?

edit: Oh, it's four years old.

8. Sep 13, 2009

### ohhohh

First use the half-angle formula to change the cos(x)^2 to (1+cos(2x))/2...
This will allow you to break the integral into two seperate problems much easier to solve
integral{ 1/2dx + integral{ cos(2x)dx
Then you will have x/2 + (sin(2x)/2) + C

9. Sep 13, 2009

### snipez90

What the, that's not even correct. If you're gonna revive a 5-year old thread, at least make sure you don't have arithmetic errors.

10. Sep 14, 2009

### chislam

sin(2x)/4 ;)

11. Feb 22, 2010

### abhishek2208

use the euler's formula

cos x= [e^ix+e^-ix ]
[-------------]
[ 2 ]

Last edited by a moderator: Mar 8, 2012
12. Feb 22, 2010