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Source: IMC 2022 Day 1 Problem 1

August 5, 2022
functioninequalitiesintegrationcalculusIMC 2022

Problem Statement

Let f:[0,1]→(0,∞)f: [0,1] \to (0, \infty) be an integrable function such that f(x)f(1−x)=1f(x)f(1-x) = 1 for all x∈[0,1]x\in [0,1]. Prove that ∫01f(x)dx≥1\int_0^1f(x)dx \geq 1.
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