1. ## Integration

I have the integral:
$\int_{0}^{4} \sin(\omega t)\cdot t^2$
I know from integrals tables that:
$\int x^2 \sin x=2x\sin x-(x^2-2)\cos x$
But i don't know to handle the (ωt) and (t) that appear in the integral

2. ## Re: Integration

Assuming $\omega$ is constant

let $k=\omega t$

$\frac{dk}{\omega}=dt$

$\int \sin(\omega t)\cdot t^2 dt= \int \sin(k)\cdot (\frac{k}{\omega})^2 \cdot \frac{dk}{\omega}$

$\frac{1}{\omega^3}\int sin(k)k^2$

3. ## Re: Integration

Yes, I will absolutely agree with the above answer try to assume W as a constant and get solution of your problem.