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Mean value of a function

  1. Aug 2, 2011 #1
    let be a function so [tex] \frac{1}{T}\int_{0}^{T}f(x)dx =0 [/tex]

    as T--->oo does it man that the function f(x) tends to ' as x--->oo what if 'f' is an oscillating function ??
     
  2. jcsd
  3. Aug 3, 2011 #2

    HallsofIvy

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    I have no clue what you mean by that. What does ' mean?

    Well, did you try an example? What if f(x)= sin(x)?

    The integral oscillates (and is bounded) but the denominator gets larger and larger. The limit is 0.
     
  4. Aug 3, 2011 #3
    I think "zetafunction" means

    [tex] \lim_{T \to \infty } \frac{1}{T} \int_{0}^{T} f(x) dx [/tex]

    Just quote my post, to see how I made it.
     
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