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Homework Help: Integration by parts homework help

  1. Mar 30, 2010 #1
    [tex]\int_0^{infinity} \ e^{-s*t}*t*cos(t) dt[/tex]

    I tried integration by parts with u=t*cost and dv=e^(-s*t) but that didn't get anywhere.

    I then tried: [tex]\L{t^n*g(t)}=(-1)^n d/ds[\int_0^{infinity} \ e^{-s*t}*cos(t) dt[/tex] but again nothing was working.

    This is a Laplace Transformation where ft=t cos(t)
     
  2. jcsd
  3. Mar 30, 2010 #2

    gabbagabbahey

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    Re: Integral

    Do you mean that you tried applying the rule

    [tex]\mathcal{L}\{t^n g(t)\}=(-1)^n\frac{d^n}{ds^n}\mathcal{L}\{g(t)\}[/tex]

    If so, that should be fairly easy, provided that you know what the Laplace transform of [itex]\cos(t)[/itex] is.
     
  4. Mar 30, 2010 #3
    Re: Integral

    The problem was I get cos(t)/(s*e^(-st)) which is in determinant and using l'hopitals rule didn't help.

    Also, the integral after separation by parts is now e time sin then you get an in determinant form with sin.
     
  5. Mar 30, 2010 #4

    gabbagabbahey

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    Re: Integral

    How on Earth are you getting something that depends on [itex]t[/itex] after integrating over [itex]t[/itex]? :confused:

    Show your work so I can see where you are going wrong.
     
  6. Mar 30, 2010 #5
    Re: Integral

    Work

    Both methods attempted

    Never mind the image won't load.
     
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