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Romania District MO 2022 Grade 12 P4

Source: Romania District MO 2022 Grade 12

March 27, 2022
Integralfunctionromaniacollege contests

Problem Statement

Let I⊆RI\subseteq \mathbb{R} be an open interval and f:I→Rf:I\to\mathbb{R} a strictly monotonous function. Prove that for all c∈Ic\in I there exist a,b∈Ia,b\in I such that c∈(a,b)c\in (a,b) and ∫abf(x) dx=f(c)⋅(b−a).\int_a^bf(x) \ dx=f(c)\cdot (b-a).
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