Calculating the Integral of (cos x)^2: Possible or Impossible?

[vadik]

Do anyone 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!

 

[mathman]

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

I'll let you finish.

 

[vadik]

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

 

[mussgo]

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

 

[HallsofIvy]

No, double angle formulas as mathman said.

 

[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

 

[awvvu]

Why does this thread have over 16,000 views?

edit: Oh, it's four years old.

 

[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 separate problems much easier to solve
integral{ 1/2dx + integral{ cos(2x)dx
Then you will have x/2 + (sin(2x)/2) + C

 

[snipez90]

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

 

[chislam]

sin(2x)/4 ;)

 

[abhishek2208]

use the euler's formula

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

 

[sponsoredwalk]

http://www.5min.com/Video/An-Introduction-to-Integrals-with-Powers-of-Sine-and-Cosine-169056088

Why doesn't the student, after nearly 6 years of unsuccessfully attempting this crazy integral, try a visual aid?

 

[Redbelly98]

This is crazy. The very first reply, post #2, answered the question. Six years ago!