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August 1st, 2017, 11:09 AM   #1
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Integration inequalities

Trying to prove the following:

Let $g(x),l(x),h(x)\geq0$ for all $x\in[a,b]$ with the inequality being strict for at least some $x_1,x_2\in[a,b]$, and let $g$'$(x)$,$l$'$(x)>0$, then

$\int_{a}^{b}h(x)g(x)l(x)dx\int_{a}^{b}h(x)dx-\int_{a}^{b}h(x)g(x)dx\int_{a}^{b}h(x)l(x)dx>0$
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