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