I took a short break from the rudin-crunching. I'm now doing reimann's integral. Anyhow here's a question I've having trouble with.(adsbygoogle = window.adsbygoogle || []).push({});

Does f^2 is integrable imply that f is integrable?

-No, take f=1 on rationals, f=-1 on irrationals on [0,1].

Does the integrability of f^3 imply that f is integrable?

I can't find a counterexample. I'm not asking for a proof but a counterexample if there is one and if there isn't just let me know!

thanks for any help.

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# Reimann Integration, squares and cubes of functions

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