Inegalitatea lui Wirtinger - caz particular

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Cezar Lupu
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Inegalitatea lui Wirtinger - caz particular

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Fie \( f:[0,1]\to\mathbb{R} \) o functie derivabila cu derivata continua astfel incat \( f(0)=f(1) \). Sa se arate ca

\( \int_0^1 (f\prime (x))^{2}dx\geq\pi^2\int_0^1 f^{2}(x)dx \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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