# Difficult integration

1. Jan 1, 2008

### raintrek

I'm probably missing something obvious here, but I'm trying to integrate the following expression;

$$\int$$sin$${^2}(kx)dx$$

I've tried doing it by part but with no luck. Is there some specific method I need to follow, or is it one of those I can only get by looking it up?

2. Jan 1, 2008

### malawi_glenn

ok this is math, not physics.

Pesonally, I would use the Euler identity for sin(kx) and then things are straight forward, or use a trig-identity. But by heart I never rememeber so many of them, so I almost always use Euler.

p.s why not using TeX 100%? :)

3. Jan 1, 2008

### George Jones

Staff Emeritus
Let me add some detail to malawi_glenn's two useful ideas.

Either write $\mathrm{sin}\left(kx\right)$ in terms of exponentials, or write $\mathrm{sin}^2\left(kx\right)$ in terms of $\mathrm{cos}\left(2kx\right)$.

4. Jan 1, 2008

### arildno

Or, as a third method, use integration by parts+cyclicity of integral.

5. Jan 2, 2008

### pam

$$\sin^2 x=[1-\cos(2x)]/2$$