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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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