MathDB
Prove this integral inequality

Source: 2019 Jozsef Wildt International Math Competition-W. 31

May 19, 2020
integrationinequalitiescalculus

Problem Statement

Let a,b∈Γa, b \in \Gamma, a<ba < b and the differentiable function f:[a,b]→Γf : [a, b] \to \Gamma, such that f(a)=af (a) = a and f(b)=bf (b) = b. Prove that ∫ab(f′(x))2dx≥b−a\int \limits_{a}^{b} \left(f'(x)\right)^2dx \geq b-a
Back to ProblemsView on AoPS