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An integral inequality

  1. Feb 14, 2007 #1
    1. The problem statement, all variables and given/known data
    suppose f(x) is monotonely decreasing and positive on [2,+∞),
    please compare [∫f(t)dt]^2 and ∫[f(t)]^2dt,
    here "∫ "means integrating on the interval [2,x]

    2. Relevant equations
    none


    3. The attempt at a solution

    Maybe the second mean value thereom of integral is helpful.
     
    Last edited: Feb 14, 2007
  2. jcsd
  3. Feb 14, 2007 #2

    HallsofIvy

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    Have you tried anything? In particular, have you selected some simple monotonically decreasing function, such as [itex]f(x)= \frac{1}{x}[/itex] and calculated those two values?
     
  4. Feb 14, 2007 #3
    In fact, yes!
    But what I'm really eager to know is how to prove the conclusion.
    Maybe when the x is large enough, [∫f(t)dt]^2 is larger.
     
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