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Integration of sine problem

  1. Dec 16, 2011 #1
    I am having problem with integration of this
    ∫sin^3πt

    This is what i tried
    ∫(1-cos^2πt)sinπt
    ∫sinπt - sinπt(cos^2πt)

    ∫sinπt - ∫sinπt(cos^2πt)

    ... and got stuck
    OR
    ∫(1-cos^2πt)sinπt
    cos^2t=(1/2)(1+cos2t) so cos^2πt=(1/2)(1+cos2π)
    ∫((1-(1/2)(1+cos2π))sinπt
    ∫1/2(sinπt) - (1/2)(cos2π)(sinπt)
    and still got stuck
    I am not even sure this is the right method to solve that.
    I know it should be (cos^3πt)/(3π) - (cosπt)/π but cannot get there

    Any help is welcome
     
  2. jcsd
  3. Dec 16, 2011 #2
    [tex]\cos x=t[/tex]
     
  4. Dec 16, 2011 #3

    SammyS

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    In my opinion, it's absolutely necessary to include the differential, in this case dt, along with integral symbol.

    Which integral are you having difficulty with?
    [itex]\displaystyle \int\sin(\pi t)\,dt[/itex]​
    or
    [itex]\displaystyle \int\sin(\pi t)\,\cos^2(\pi t)\,dt\ ?[/itex]​

    For the second one, let u = cos(πt) , then du = _?_
     
  5. Dec 17, 2011 #4
    Great. That was quite easy. Thank you very much
     
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