Basic Analysis I — Real Analysis · Problem 5.2.6

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · properties-of-integral

Problem

Let f:[a,b]→Rf : [a,b] \to \mathbb{R} be a continuous function and ∫abf=0\int_a^b f = 0. Prove that there exists a c∈[a,b]c \in [a,b] such that f(c)=0f(c) = 0. (Compare with the previous exercise.)

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