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Consider the following integral: (³ In(2x) dx.

Consider the following integral: (³ In(2x) dx.

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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Question
Consider the following integral: S³₁ (a) Why is this integral improper? Choose the best answer. 3. A. Because lim ln(2x) = ∞. t→∞ B. Because ln(2x) is not the derivative of an elementary function. A. It diverges. 774 B. In(2x) dx. C. Because the domain of ln(2x) is not the en- tire real line. (b) Find the value of this improper integral, if it converges. C. 1 1 D. D. Because ln(2x) has a vertical asymptote at x = 0. E. Because In (2x) is zero at x = F. Because In (2x) has a horizontal asymptote. E. -2 F. -1 1/2.
Transcribed Image Text:Consider the following integral: S³₁ (a) Why is this integral improper? Choose the best answer. 3. A. Because lim ln(2x) = ∞. t→∞ B. Because ln(2x) is not the derivative of an elementary function. A. It diverges. 774 B. In(2x) dx. C. Because the domain of ln(2x) is not the en- tire real line. (b) Find the value of this improper integral, if it converges. C. 1 1 D. D. Because ln(2x) has a vertical asymptote at x = 0. E. Because In (2x) is zero at x = F. Because In (2x) has a horizontal asymptote. E. -2 F. -1 1/2.
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