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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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[Integrability: Riemann and Darboux] How do you prove this? I was told this can be done in a couple lines.
Need this done ASAP, thank you! Will upvote answer if done within 30 minutes!
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5817aa11-0184-4c5d-8844-a1713e3e9507%2F71712544-83c5-4f11-98dc-34353e045514%2Fagam6zd_processed.png&w=3840&q=75)
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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