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[obm-l] Provar que Integral (0 a 2pi) f(x) cos(x) dx >= 0

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Subject: [obm-l] Provar que Integral (0 a 2pi) f(x) cos(x) dx >= 0
From: Artur Costa Steiner <artur.steiner@xxxxxxxxxx>
Date: Wed, 18 Jun 2008 15:51:30 -0300
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Acho este problema interessante:

Suponhamos que f:R --> R seja convexa e derivável em R. Mostre que  Integral (0 a 2pi) f(x) cos(x) dx >= 0. Em que casos teremos igualdade?

Artur

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