Suppose that f is integrable on [a, b] and g is integrable on [b, c]. Letf(x) x [a,b)h: [a, c] → R be defined by f(x)=2022x=bg(x) x (b, c]Prove that h is integrable on [a, c] and find its integral.

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Answered: Suppose that f is integrable on [a, b]…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 17E: If e is the unity in an integral domain D, prove that (e)a=a for all aD. [Type here][Type here]

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Suppose that f is integrable on [a, b] and g is integrable on [b, c]. Let f(x) x [a,b) h: [a, c] → R be defined by f(x)=2022 x=b g(x) x (b, c] Prove that h is integrable on [a, c] and find its integral.