(a) Prove that if g(x) := 0 for 0 < x < 1/2 and g(x) := 1...

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(a) Prove that if g(x) := 0 for 0 < x < 1/2 and g(x) := 1 for 1/2 < x < 1, then the Darboux integral of g on [0, 1] is equal to 1/2.
(b) Does the conclusion hold if we change the value of g at the point 1/2 to 13?

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 11:06 AM

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(a) Prove that if g(x) := 0 for 0 < x < 1/2 and g(x) := 1...

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Introduction to Real Analysis

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