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Determine continuous functions

Source: RMO 2004, Grade 12, Problem 1

February 26, 2006
functionintegrationcalculusderivativelimitalgebrafunctional equation

Problem Statement

Find all continuous functions f:R→Rf : \mathbb R \to \mathbb R such that for all x∈Rx \in \mathbb R and for all n∈N∗n \in \mathbb N^{\ast} we have n2∫xx+1nf(t) dt=nf(x)+12. n^2 \int_{x}^{x + \frac{1}{n}} f(t) \, dt = n f(x) + \frac12 . Mihai Piticari
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