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

I need to find 2 functions on [0,1]: one that is integrable, one that isn't, such that their product is integrable.

I'd like to use functions that are non-constant, if possible

2. Relevant equations

3. The attempt at a solution

I was thinking of using

g(x) := x-1

h(x) := 1/(x-1)

... But I'm having trouble proving h(x) is not integrable on [0,1]...

I used the fact that g was monotone to prove it is integrable and obviously gh is integrable because it's constant. Right now we're looking at Riemann integrals, but I don't know how to state the proof...

Please help!

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# Homework Help: Integrable Functions

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