Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n> 1 is some integer. (i) Explain why f(n - 1) < f(x) dx < f(n) n-1 By considering areas bounded by the y-axis, evaluate L in In x dx n-1 i) Hence show that n-1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(c) Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n >1 is some
integer.
(i) Explain why
f(n – 1) <
f (x) dx < f(n)
1/-
(ii) By considering areas bounded by the y-axis, evaluate
In x dx
n-1
(iii) Hence show that
n
n-1
くe<
n - 1
Transcribed Image Text:(c) Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n >1 is some integer. (i) Explain why f(n – 1) < f (x) dx < f(n) 1/- (ii) By considering areas bounded by the y-axis, evaluate In x dx n-1 (iii) Hence show that n n-1 くe< n - 1
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