integration

**turtle** · February 5th 2007, 04:29 PM

Can someone please help me integrate 1 - (cos x)^2 ?
Thanks!

**ThePerfectHacker** · February 5th 2007, 04:33 PM

Originally Posted by turtle

Can someone please help me integrate 1 - (cos x)^2 ?
Thanks!

You can write,
$\int (1+\cos x)(1-\cos x) dx$
By difference of two squares.
Now, use integration by parts.

**AlvinCY** · February 5th 2007, 05:47 PM

There's nothing wrong with what TPH is doing :-),

I personally hate integration by parts. It's long and dreaful, personally:

$\int 1 - cos^2 x\,dx$
$=\int sin^2 x\,dx$ , using double angle formula for cos2x,
$=\int \frac{1 - cos2x}{2}\,dx$
$=\int \frac{1}{2} - \frac{cos2x}{2}\,dx$
$=\frac{x}{2} - \frac{sin2x}{4} + C$

Tada!

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