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Math Help - Integral of t cos pi t

  1. #1
    Newbie
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    Mar 2009
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    Integral of t cos pi t

    I am working on a hw problem for multivariable calc that I can't figure out

    If r(t)=(t^2)i + (tcospit)j + (sinpit)k
    Evaluate integral r(t) from 0 to 1.

    I understand that if the vector is composed of 3 component functions, then the integral of the vector is the integrals of the component functions.

    So I have (1/3 t^3)i + (integral tcospit)j + (-1/pi cospit)k evaluated from 0 to 1.

    I can't figure out integral tcospit. Is there a substituition I am missing or an identity I can use?

    Thank
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    You need to integrate by parts
    \int t\:\cos\left(\pi t\right) dt

    using
    u = t and dv = \cos\left(\pi t\right) dt
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