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Show that 2f E R[a, b] and | [2f(x)] dx = 2 e| f(x) dz. 2.

Show that 2f E R[a, b] and | [2f(x)] dx = 2 e| f(x) dz. 2.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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[Integrability: Riemann and Darboux] How do you prove 2? I was told this can be done in a couple lines.

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Let f E R[a, b] (which implies that f is bounded). 1. For any partition of a, b], show that U (2f, P) = 2U(f, P), L(2f,P)=2L(f, P). 2. Show that 2f E R[a, b] and [2f(x)] dx f(x) dx. = 2 a
Transcribed Image Text:Let f E R[a, b] (which implies that f is bounded). 1. For any partition of a, b], show that U (2f, P) = 2U(f, P), L(2f,P)=2L(f, P). 2. Show that 2f E R[a, b] and [2f(x)] dx f(x) dx. = 2 a
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