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

  • #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?
 

Answers and Replies

  • #2
105
0
f(x)=1 for rational x
f(x)=-1 for irrational x

Is it Riemann integrable?
 

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