设 $p(x) \in C[a, b]$ 非负, $f, g \in C[a, b]$ 且单增.
证明:
$\int_a^b p(x) f(x) \mathrm{d} x \int_a^b p(x) g(x) \mathrm{d} x \leq \int_a^b p(x) \mathrm{d} x \int_a^b p(x) f(x) g(x) \mathrm{d} x$
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$\text{C.}$
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$\text{F.}$