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: Let f [a, b] → R be a bounded function. Then f : [a, b] → R is Riemann integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. n1x In this case, the Riemann integral of f over [a, b] can be computed by S ["¹= f = lim L(f, Pn) = lim U(f, Pn). n1x n→∞ a (4.1) (4.2)

: Let f [a, b] → R be a bounded function. Then f : [a, b] → R is Riemann integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. n1x In this case, the Riemann integral of f over [a, b] can be computed by S ["¹= f = lim L(f, Pn) = lim U(f, Pn). n1x n→∞ a (4.1) (4.2)

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 [a, b] → R be a bounded function. Then f [a, b] → R is Riemann ! integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) L(f, Pn)) = 0. (4.1) n→∞ In this case, the Riemann integral of f over [a, b] can be computed by a 1 = lim L(f, Pn) n-x = lim U(f, Pn). n→∞ (4.2)
Transcribed Image Text:Let f [a, b] → R be a bounded function. Then f [a, b] → R is Riemann ! integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) L(f, Pn)) = 0. (4.1) n→∞ In this case, the Riemann integral of f over [a, b] can be computed by a 1 = lim L(f, Pn) n-x = lim U(f, Pn). n→∞ (4.2)
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