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Improper Integrals, Infinite Limits

  1. Mar 10, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫e-Sxsin(ax) dx, S and A are constants, upper limit is ∞ lower is 0

    2. Relevant equations

    ∫ u dv = uv - ∫ vdu

    3. The attempt at a solution

    After integrating by parts twice I got:

    (S2)/S(S2+a2) lim c→∞ [-sin(ax)e-Sx + acos(ax)e-Sx] |[itex]^{C}_{0}[/itex]

    Okay, now how on earth do I take the lim c→∞ if sin(ax) is periodic? Since limx→∞ e^-x=0 would it just be (S2)/S(S2+a2) [(0+0) - (0+1)] which becomes
    -(S2)/S(S2+a2)?
     
    Last edited: Mar 10, 2013
  2. jcsd
  3. Mar 10, 2013 #2

    SammyS

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    sin(ax) is bounded.

    -1 ≤ sin(ax) ≤ 1
     
  4. Mar 11, 2013 #3
    Yeah I know but how do you take the limit of something that's bounded by two numbers? I'm assuming you can't. What I got was that since limx→∞ e^-x=0 would it just be (S2)/S(S2+a2) [(0+0) - (0+1)]? which becomes -(S2)/S(S2+a2). I just want to verify that this is the answer.
     
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