Prove that if f is (Lebesgue-) integrable and the Improper Riemann Integral of f on [a, b] exists then the two integrals are equal. (Hint: Consider fn=fXa+1/n, & when a is finite and gn = fx-n, s if a The same can be done for b.) b
Prove that if f is (Lebesgue-) integrable and the Improper Riemann Integral of f on [a, b] exists then the two integrals are equal. (Hint: Consider fn=fXa+1/n, & when a is finite and gn = fx-n, s if a The same can be done for b.) b
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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![1. Prove that if f is (Lebesgue-) integrable and the Improper Riemann
Integral of f on [a, b] exists then the two integrals are equal. (Hint:
Consider fn=fXa+1/n, b when a is finite and gn = fx-n, & if a = -0.
The same can be done for b.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47456ed3-eb8f-43e4-a5c7-fb8562737ff3%2F23018889-ea73-4e1e-9daa-7a0d2611f496%2Fsv3vdv8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Prove that if f is (Lebesgue-) integrable and the Improper Riemann
Integral of f on [a, b] exists then the two integrals are equal. (Hint:
Consider fn=fXa+1/n, b when a is finite and gn = fx-n, & if a = -0.
The same can be done for b.)
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