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).

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 continuous on \([a, b]\), then there exists \( y \) in \((a, b)\) such that 

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