Prove the integral mean value theorem: if \( f \) is continuous on \([a, b]\), then there exists \( y \) in \((a, b)\) such that \[ \int_a^b f(x) \, dx = (b-a)f(y).\]

Answered: Prove the integral mean value theorem:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Prove the integral mean value theorem: if f is continous on [a, b), then there exists y in (a, b) such that f(x) dx = (b – a)f(y).