Fie \( f:[0,1]\rightarrow\mathbb{R} \) ,continua.Sa se arate ca :\( \frac{1}{4}\int_0^1 f^2(x)dx+2(\int_0^1 f(x)dx)^2\ge 3\int_0^1 f(x)dx\int_0^1 xf(x)dx \).
Cezar Lupu,Shortlist ONM 2007
Inegalitate integrala
Moderators: Bogdan Posa, Beniamin Bogosel, Marius Dragoi
-
Laurentiu Tucaa
- Thales
- Posts: 145
- Joined: Sun Mar 22, 2009 6:22 pm
- Location: Pitesti
-
Marius Mainea
- Gauss
- Posts: 1077
- Joined: Mon May 26, 2008 2:12 pm
- Location: Gaesti (Dambovita)
-
Laurentiu Tucaa
- Thales
- Posts: 145
- Joined: Sun Mar 22, 2009 6:22 pm
- Location: Pitesti
-
Marius Mainea
- Gauss
- Posts: 1077
- Joined: Mon May 26, 2008 2:12 pm
- Location: Gaesti (Dambovita)