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Theorem: Mean Value Theorem For Riemann Integrals

Let \([a,b]\) be a closed real interval and let \(f,\phi:[a,b]\mapsto\mathbb R\) be continuous functions with \(\phi(x)\ge 0\) for all \(x\in[a,b]\). Then there exists a value (mean value) \(\xi\in[a,b]\) such that


For the special case \(\phi(x)=1\) for all \(x\in[a,b]\), we have


| | | | | created: 2016-03-06 20:11:33 | modified: 2016-03-06 20:18:03 | by: bookofproofs | references: [581]

1.Proof: (related to "Mean Value Theorem For Riemann Integrals")

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983