If av(ƒ) really is a typical value of the integrable

Chapter 5, Problem 81E

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QUESTION:

If av(ƒ) really is a typical value of the integrable function ƒ(x) on [a, b], then the constant function av(ƒ) should have the same integral over [a, b] as ƒ. Does it? That is, does

\(\int_{a}^{b} a v(f) d x=\int_{a}^{b} f(x) d x ?\)

Give reasons for your answer.

Equation Transcription:

Text Transcription:

integral _a ^b av(f) dx=integral _a ^b f(x) dx?

Questions & Answers

QUESTION:

If av(ƒ) really is a typical value of the integrable function ƒ(x) on [a, b], then the constant function av(ƒ) should have the same integral over [a, b] as ƒ. Does it? That is, does

\(\int_{a}^{b} a v(f) d x=\int_{a}^{b} f(x) d x ?\)

Give reasons for your answer.

Equation Transcription:

Text Transcription:

integral _a ^b av(f) dx=integral _a ^b f(x) dx?

ANSWER:

Solution

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