(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f be positive and bounded over [a,b]. If f^2 is integrable over [a,b], then show that f is as well.

3. The attempt at a solution

I'm just trying to use the fact that the upper and lower sums of f^2 over a partition P are arbitrarily close, and then somehow find an upper bound for the difference of the upper and lower sums of f based on that. I've tried separating it into cases, where the max and min of f on an interval are >=1, <1, etc. but it hasn't really led anywhere. If anyone could give me some sort of hint, i'd really appreciate it =)

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# Homework Help: Integrability of f^2

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