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Math Help - Integration

  1. #1
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    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
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  2. #2
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    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
    Thanks from HallsofIvy
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  3. #3
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    Re: Integration

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