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Limit of integrable functions

  1. Dec 11, 2008 #1
    Prove: If f is integrable on [a , b] then
    lim f =0
    x[tex]\rightarrow[/tex]a+

    the integral goes from a to x.

    How do i go about and prove this? I'm confused.
    Please help me out!
    Thank You
     
    Last edited: Dec 11, 2008
  2. jcsd
  3. Dec 11, 2008 #2

    HallsofIvy

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    Re: integrable?

    Do you mean
    [tex]\lim_{x\rightarrow a^+} \int_a^x f(t)dt= 0[/tex]

    The way you have written it, that the limit of f is 0, makes no sense- that certainly is not necessarily true.

    My suggestion here is the same as to your other question: use the definition of integral in terms of Riemann sums.
     
  4. Dec 15, 2008 #3
    Re: integrable?

    I've never learn Riemann sum definition.
    What is that?
     
  5. Dec 15, 2008 #4

    HallsofIvy

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    Re: integrable?

    First, is what I wrote what you mean. And if you have never learned Riemann sums, what definition of [itex]\int_a^b f(x)dx[/itex] are you using?
     
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