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integral fog=integral gof

Source: Bogdan Stan 2011

October 7, 2019
functionintegrabilityriemann integralcalculusintegration

Problem Statement

Find all Riemann integrable functions f:R⟶R f:\mathbb{R}\longrightarrow\mathbb{R} which have the property that, for all nonconstant and continuous functions g:R⟶R, g:\mathbb{R}\longrightarrow\mathbb{R}, and all real numbers a,b a,b such that a<b, a<b, the following equality holds. ∫ab(f∘g)(x)dx=∫ab(g∘f)(x)dx \int_a^b \left( f\circ g \right) (x)dx=\int_a^b \left( g\circ f \right) (x)dx
Cosmin Nițu
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