# Integration

• May 4th 2013, 02:20 PM
Karol
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
• May 4th 2013, 02:56 PM
Shakarri
Re: Integration
Assuming $\omega$ is constant

let $k=\omega t$

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

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

$\frac{1}{\omega^3}\int sin(k)k^2$
• Jan 30th 2014, 01:34 AM
AnnyIngram
Re: Integration
Yes, I will absolutely agree with the above answer try to assume W as a constant and get solution of your problem.