# Homework Help: Integration of sine problem

1. Dec 16, 2011

### greg997

I am having problem with integration of this
∫sin^3πt

This is what i tried
∫(1-cos^2πt)sinπt
∫sinπt - sinπt(cos^2πt)

∫sinπt - ∫sinπt(cos^2πt)

... and got stuck
OR
∫(1-cos^2πt)sinπt
cos^2t=(1/2)(1+cos2t) so cos^2πt=(1/2)(1+cos2π)
∫((1-(1/2)(1+cos2π))sinπt
∫1/2(sinπt) - (1/2)(cos2π)(sinπt)
and still got stuck
I am not even sure this is the right method to solve that.
I know it should be (cos^3πt)/(3π) - (cosπt)/π but cannot get there

Any help is welcome

2. Dec 16, 2011

### Karamata

$$\cos x=t$$

3. Dec 16, 2011

### SammyS

Staff Emeritus
In my opinion, it's absolutely necessary to include the differential, in this case dt, along with integral symbol.

Which integral are you having difficulty with?
$\displaystyle \int\sin(\pi t)\,dt$​
or
$\displaystyle \int\sin(\pi t)\,\cos^2(\pi t)\,dt\ ?$​

For the second one, let u = cos(πt) , then du = _?_

4. Dec 17, 2011

### greg997

Great. That was quite easy. Thank you very much