I'm looking for a function
f:[a,b] -> R such that |f| and f2 are integrable on [a,b]
To start with, f must be discontinuous (a continuous function on a closed interval is integrable). Can you think of a function f such that f is discontinuous, but |f| (and thus f2 = |f|2) is continuous?
This is really an analysis question, so it really belongs in that forum. :)
f(x)= 1 for x rational,
-1 for x irational
Don't just give him an answer. ;)
(That's the exact same function I was thinking of, though.)
I forgot to say: Only if you are dealing with newton or rieman integrals, otherwise f(x) is integrable.
Oh I don't know why I didn't think of that!!
Thank you so much to both of youuuu!
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