# Sqrtf Math Homework

I'm having trouble proving or finding a counterexample for the following statement:

If $f>0$ is integrable on $[a,b]$ then $\sqrt{f}$ is integrable

We're using the Riemann integral definition:

If $f$ is integrable on $[a,b]$ then given $\epsilon>0$ there exists a $\delta>0 \ $ s.t. if $P$ is a partition of $[a,b]$ and $\lambda(P)<\delta$ then $|S-I|<\epsilon \ $ (where $S$ is the Riemann sum and $I$ is the integral's value).

I tried using the fact that $\sqrt{x}$ is uniformly continuous on $(0,\infty)$ which means that if $f$'s oscillation gets very small, so does $\sqrt{f}$'s, but I wasn't able to rigorously prove it.

Is this statement actually true? is the uniformly continuous angle of any help?

Much appreciated.

integration

asked Apr 14 '13 at 7:44

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