Let $f,g \in C[0,1]$, such that $f,g \geq0$, do we have the following inequality $$\sqrt{\int_0^1 fg\,dx} \leq \int_0^1 f\,dx \int_0^1 g\,dx.$$ Or in other words can we at least say that
$$\int_0^1 fg\,dx \leq \int_0^1f\,dx\int_0^1g\,dx.$$
2026-04-06 04:41:01.1775450461
Integration inequality $\int_0^1 fg\,dx \leq \int_0^1f\,dx\int_0^1g\,dx$
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