3.2 † Prove part (ii) of Theorem 3.1.2. Theorem 3.1.2 Let f and g be in R[a, 6} and c e R. Then i. f+g€ R[a, b) and (f + g)(x) dx = f(x) dr + | 9(x) dr. ii. cf e Rla, b] and | ef(2) dz = c f(2) dzr.
3.2 † Prove part (ii) of Theorem 3.1.2. Theorem 3.1.2 Let f and g be in R[a, 6} and c e R. Then i. f+g€ R[a, b) and (f + g)(x) dx = f(x) dr + | 9(x) dr. ii. cf e Rla, b] and | ef(2) dz = c f(2) dzr.
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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![3.2 † Prove part (ii) of Theorem 3.1.2.
Theorem 3.1.2 Let f and g be in R[a, 6} and c e R. Then
i. f+g€ R[a, b) and
(f + g)(x) dx =
f(x) dr +
|
9(x) dr.
ii. cf e Rla, b] and
cf(r) dr](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadd5b56d-97e3-4d3c-9aa9-5b563ad77377%2F4bac3108-4e2a-438f-8502-8a1e61aecd98%2Fqfpkcoj_processed.png&w=3840&q=75)
Transcribed Image Text:3.2 † Prove part (ii) of Theorem 3.1.2.
Theorem 3.1.2 Let f and g be in R[a, 6} and c e R. Then
i. f+g€ R[a, b) and
(f + g)(x) dx =
f(x) dr +
|
9(x) dr.
ii. cf e Rla, b] and
cf(r) dr
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