# Thread: Examples of Riemann integrable functions

1. ## Examples of Riemann integrable functions

I'm no good at coming up with examples... please help...

a. Give an example of a function f: [0,2] $\rightarrow$ R such that f isn't Riemann integrable on [0,2], but |f| is.

b. Give an example of a function f: [0,2] $\rightarrow$ R such that f isn't Riemann integrable on [0,2], but $f^2$ is.

c. Give an example of two functions f,g : [0,1] $\rightarrow$ R such that f is Riemann integrable on [0,1], but g isn't and fg is Riemann integrable on [0,1].

2. Let $f(x)= 1$ if $x\in \mathbb{Q}$ and $f(x)=-1$ if $x\in \mathbb{R} \setminus \mathbb{Q}$ and $g\equiv 0$

3. wouldn't g be the one that's integrable in that case? I assume I would just swap the f(x) and the g(x)