1) Let f be integrable on an interval [a, b] (with a < b). Let m and M be the infimum and surpemum of f on [a, b], respectively. Prove, from the definition of integral that m(b – a) < | f(x) dr < M(b – a).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.1: Numerical Integration
Problem 21E
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(1) Let f be integrable on an interval [a, b] (with a < b). Let m and M be the infimum and
surpemum of f on [a, b], respectively. Prove, from the definition of integral that
m(b – a) :
f(x) dr < M(b – a).
Ja
Transcribed Image Text:(1) Let f be integrable on an interval [a, b] (with a < b). Let m and M be the infimum and surpemum of f on [a, b], respectively. Prove, from the definition of integral that m(b – a) : f(x) dr < M(b – a). Ja
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