Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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please prove every step and don't use other one's answer thank yoi

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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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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