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Let f be a bounded function on [a, b]. Show that f is integrable on [a, b] if and only if there is a sequence of partitions (Pn) of the interval [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. 31-00

Let f be a bounded function on [a, b]. Show that f is integrable on [a, b] if and only if there is a sequence of partitions (Pn) of the interval [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. 31-00

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let f be a bounded function on [a, b]. Show that f is integrable on [a, b] if and only if there is a sequence of partitions {Pn} of the interval [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. n→∞0
Transcribed Image Text:Let f be a bounded function on [a, b]. Show that f is integrable on [a, b] if and only if there is a sequence of partitions {Pn} of the interval [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. n→∞0
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