I have the integral:
$\displaystyle \int_{0}^{4} \sin(\omega t)\cdot t^2$
I know from integrals tables that:
$\displaystyle \int x^2 \sin x=2x\sin x-(x^2-2)\cos x$
But i don't know to handle the (ωt) and (t) that appear in the integral
Assuming $\displaystyle \omega$ is constant
let $\displaystyle k=\omega t$
$\displaystyle \frac{dk}{\omega}=dt$
$\displaystyle \int \sin(\omega t)\cdot t^2 dt= \int \sin(k)\cdot (\frac{k}{\omega})^2 \cdot \frac{dk}{\omega}$
$\displaystyle \frac{1}{\omega^3}\int sin(k)k^2$