MathDB

Integral identity-inequality

Source: Moldova MO 2007 12th grade day II problem 8

March 4, 2007

calculusintegrationinequalitiesfunctionreal analysisreal analysis unsolved

Problem Statement

Find all continuous functions

f\colon [0;1] \to R

such that

\int_{0}^{1}f(x)dx = 2\int_{0}^{1}(f(x^{4}))^{2}dx+\frac{2}{7}