(a) For f(x) > 0 and differentiable on [a, b], show th = In(f(x)) is given by F(x))² + (f"(x))² L = f(x) xp- b) Use the result in part 2(a) to find the length of y In(sin x)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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"(a) For f(x) > 0 and differentiable on [a, b], show the length, L, of the curve
y = In(f(x)) is given by
VC(x))² + (f'(x))²
dx
f(x)
(b) Use the result in part 2(a) to find the length of y = In(sin x), n/4 < x < n/2
Transcribed Image Text:"(a) For f(x) > 0 and differentiable on [a, b], show the length, L, of the curve y = In(f(x)) is given by VC(x))² + (f'(x))² dx f(x) (b) Use the result in part 2(a) to find the length of y = In(sin x), n/4 < x < n/2
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