Lebl-Basic-Analysis-I · Problem 5.2.7

The Riemann Integral

Mathematics · properties-of-integral

Problem

Let f:[a,b]→Rf : [a,b] \to \mathbb{R} and g:[a,b]→Rg : [a,b] \to \mathbb{R} be continuous functions such that ∫abf=∫abg\int_a^b f = \int_a^b g. Show that there exists a c∈[a,b]c \in [a,b] such that f(c)=g(c)f(c) = g(c).

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