Basic Analysis I — Real Analysis · Problem 5.2.7

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · 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).

Browse the problem library