- #1
Damidami
- 94
- 0
Is it true that
[itex] \int_0^1 f(x) dx \in \mathbb{Q} \Rightarrow \int_0^1 x f(x) dx \in \mathbb{Q} [/itex]
?
(Suppose [itex] f(x) [/itex] integrable as needed)
I thought of this conjecture yesterday and still couldn't prove it, I tried using integration by parts to relate it to the original, but didn't work.
Any ideas? Or counterexamples?
Thanks!
[itex] \int_0^1 f(x) dx \in \mathbb{Q} \Rightarrow \int_0^1 x f(x) dx \in \mathbb{Q} [/itex]
?
(Suppose [itex] f(x) [/itex] integrable as needed)
I thought of this conjecture yesterday and still couldn't prove it, I tried using integration by parts to relate it to the original, but didn't work.
Any ideas? Or counterexamples?
Thanks!