Lebl-Basic-Analysis-I · Problem 5.2.5

The Riemann Integral

Mathematics · properties-of-integral

Problem

Let f:[a,b]→Rf : [a,b] \to \mathbb{R} be a continuous function such that f(x)≥0f(x) \geq 0 for all x∈[a,b]x \in [a,b] and ∫abf=0\int_a^b f = 0. Prove that f(x)=0f(x) = 0 for all xx.

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