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(a) Let a ≥ 2 be a real number. By considering appropriate trapeziums, show that In(a − 1) + In a 2 그를 In x dx ≤ In a and (b) Using the result from (a), deduce that for every integer n ≥ 2. fo In x dx > Linxdx In x dx ≤ ln(n!) - Inn ≤ "In In x dx

(a) Let a ≥ 2 be a real number. By considering appropriate trapeziums, show that In(a − 1) + In a 2 그를 In x dx ≤ In a and (b) Using the result from (a), deduce that for every integer n ≥ 2. fo In x dx > Linxdx In x dx ≤ ln(n!) - Inn ≤ "In In x 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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(a) Let a ≥ 2 be a real number. By considering appropriate trapeziums, show that C-X "In x dx ≤ In a and (b) Using the result from (a), deduce that Lin for every integer n ≥ 2. C.- In x dx > In(a - 1) + In a 2 In x dx ≤ In(n!) - Inn ≤ -inns [*inxdx 1
Transcribed Image Text:(a) Let a ≥ 2 be a real number. By considering appropriate trapeziums, show that C-X "In x dx ≤ In a and (b) Using the result from (a), deduce that Lin for every integer n ≥ 2. C.- In x dx > In(a - 1) + In a 2 In x dx ≤ In(n!) - Inn ≤ -inns [*inxdx 1
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