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Homework Help: Integral from o to inf of sin(x/2)dx

  1. Feb 23, 2010 #1
    Integral from o to inf of sin(x/2)dx

    First thing I did was ditch the infinity so it became:
    lim as a-->inf of integral from 0 to a of sin(x/2)dx

    next I integrated it:
    lim as a approaches infin of -cos(x/2) evaluated from o to a

    then I plugged in:
    lima->inf of -2cos(a/2)+2(cos0)

    My problem is that I don't know if cos of inf diverges of converges. I know that it occelates, but what does that count as? Or, am I missing a step in here or just messed up somewhere along way? If anyone has any suggestions, I would greatly appreciate it.
  2. jcsd
  3. Feb 23, 2010 #2


    Staff: Mentor

    Re: convergence

    You can't take the cosine of infinity. The limit of interest, lim a --> inf -2cos(a/2) does not exist, so your original integral diverges.
  4. Feb 23, 2010 #3
    Re: convergence

    ok Thank you!
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