# Bounded Function being absolutely integrable but not integrable

1. Feb 3, 2009

### jdz86

1. The problem statement, all variables and given/known data

If f:[a,b] $$\rightarrow$$ $$\Re$$ is bounded then so is |f|, where |f|(x) = |f(x)|. Call f absolutely integrable if |f| is integrable on [a,b]. Give an example of a bounded function which is absolutely integrable but not integrable.

2. Relevant equations

None

3. The attempt at a solution

I was thinking $$\sqrt{x}$$ but was unsure of how to show it.

2. Feb 3, 2009

### Dick

How about looking for a nonintegrable function that takes only the values +1 and -1?