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A function f that is not Riemann integrable but |f| is Riemann integrable?

  1. Aug 10, 2011 #1
    I was just going over Riemann integrability and how to prove it, and was just wondering is it possible to have a function f that is not Riemann integrable but |f| is Riemann integrable? Say on an interval [0,1] for example. (as that is what most examples I have done are on so easiest for me to compare)
    How would this work? Or does it not?
     
  2. jcsd
  3. Aug 10, 2011 #2
    f(x)=1 for rational x
    f(x)=-1 for irrational x

    Is it Riemann integrable?
     
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