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

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- May 4th 2013, 01:20 PMKarolIntegration
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 - May 4th 2013, 01:56 PMShakarriRe: Integration
Assuming $\displaystyle \omega$ is constant

let $\displaystyle k=\omega t$

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

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

$\displaystyle \frac{1}{\omega^3}\int sin(k)k^2$ - Jan 30th 2014, 12:34 AMAnnyIngramRe: Integration
Yes, I will absolutely agree with the above answer try to assume W as a constant and get solution of your problem.