Basic Analysis I — Real Analysis · Problem 5.3.9

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · fundamental-theorem-of-calculus

Problem

Suppose f:[a,b]→Rf : [a,b] \to \mathbb{R} is continuous and ∫axf=0\int_a^x f = 0 for all rational xx in [a,b][a,b]. Show that f(x)=0f(x) = 0 for all x∈[a,b]x \in [a,b].

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