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