MathDB
Miklos Schweitzer 1973_6

Source:

November 12, 2008
functionintegrationsearchreal analysisreal analysis unsolved

Problem Statement

If f f is a nonnegative, continuous, concave function on the closed interval [0,1] [0,1] such that f(0)=1 f(0)=1, then 01xf(x)dx23[01f(x)dx]2. \int_0^1 xf(x)dx \leq \frac 23 \left[ %Error. "diaplaymath" is a bad command. \int_0^1 f(x)dx \right]^2. Z. Daroczy