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Homework Help: HELP: Integral

  1. Dec 8, 2008 #1
    Limit of an integral
    1. The problem statement, all variables and given/known data
    the limit as n goes to [tex]\infty[/tex] of
    [tex]\int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx[/tex]
    dx is the lebesgue measure

    2. Relevant equations
    I thought I could use the monotone convergence theorem or the dominated convergence theorem neither work.

    3. The attempt at a solution
    the intregrand is dominated by [tex]1/\sqrt{x}[/tex] but [tex]1/\sqrt{x}[/tex] isn't lebesgue integrable.
  2. jcsd
  3. Dec 8, 2008 #2


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    Science Advisor

    ?? [itex]1/\sqrt{x}= x^{-1/2}[/itex] surely is Lebesque integrable on [0,1]. In fact, it is Riemann integrable and its integral from 0 to 1 is just [itex]\left 2x^{1/2}\right|_{x=0}^1= 2[/itex].
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