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Bounded Function being absolutely integrable but not integrable

  1. Feb 3, 2009 #1
    1. The problem statement, all variables and given/known data

    If f:[a,b] [tex]\rightarrow[/tex] [tex]\Re[/tex] is bounded then so is |f|, where |f|(x) = |f(x)|. Call f absolutely integrable if |f| is integrable on [a,b]. Give an example of a bounded function which is absolutely integrable but not integrable.

    2. Relevant equations


    3. The attempt at a solution

    I was thinking [tex]\sqrt{x}[/tex] but was unsure of how to show it.
  2. jcsd
  3. Feb 3, 2009 #2


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    How about looking for a nonintegrable function that takes only the values +1 and -1?
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