Inegalitatea lui Wirtinger - caz particular
Posted: Thu Jan 31, 2008 12:43 am
Fie \( f:[0,1]\to\mathbb{R} \) o functie derivabila cu derivata continua astfel incat \( f(0)=f(1) \). Sa se arate ca
\( \int_0^1 (f\prime (x))^{2}dx\geq\pi^2\int_0^1 f^{2}(x)dx \).
\( \int_0^1 (f\prime (x))^{2}dx\geq\pi^2\int_0^1 f^{2}(x)dx \).