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Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

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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Use a comparison test to determine whether 1 (ln(x) — 1) dx converges or diverges.
Transcribed Image Text:Use a comparison test to determine whether 1 (ln(x) — 1) dx converges or diverges.
Expert Solution
Step 1: Comparison test:

(i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. 

(ii) If f(x)≥g(x),∀x∈[a,∞) and ∫a∞g(x)dx is divergent,  then ∫a∞f(x)dx is divergent. 

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