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[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!

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# A conjecture about the rationallity of a definite integral

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