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Math Help - Proving function is not integrable

  1. #1
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    Proving function is not integrable

    S(x) = x - n where n<= x <= n+1

    How do I show that there is no function F such that F'=S?
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    MHF Contributor chisigma's Avatar
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    Re: Proving function is not integrable

    Quote Originally Posted by BrownianMan View Post
    S(x) = x - n where n<= x <= n+1

    How do I show that there is no function F such that F'=S?
    S(x) is known as 'fractional part of x'...

    Fractional Part -- from Wolfram MathWorld

    ... and it seems not to exist a valid reason for which it is not integrable...

    Kind regards

    \chi \sigma
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  3. #3
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    Re: Proving function is not integrable

    Quote Originally Posted by BrownianMan View Post
    S(x) = x - n where n<= x <= n+1

    How do I show that there is no function F such that F'=S?
    S can't be a derivative because it has jump discontinuities at \mathbb{Z}, and derivatives satisfy the mean value property. On the other hand it's integrable over any bounded interval. I suggest youu review what the fundamental theorem of calculus actually says.
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