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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![72. (a) Use integration by parts to show that
S S(x) dx = xf(x) – f xf(x) dx
%3D
(b) If f and g are inverse functions and f' is continuous,
prove that
) dx = bf(b) – af (a) – S g(v) dy
%3D
Jf (a)
[Hint: Use part (a) and make the substitution y = f(x).]
(c) In the case where f and g are positive functions and
b > a > 0, draw a diagram to give a geometric interpre-
tation of part (b).
(d) Use part (b) to evaluate In x dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84577f47-6855-4e4f-91d0-241ebc051b86%2F8069f377-fdfe-4d55-a905-51ed3bdd469e%2Fwikyr7c_processed.png&w=3840&q=75)
Transcribed Image Text:72. (a) Use integration by parts to show that
S S(x) dx = xf(x) – f xf(x) dx
%3D
(b) If f and g are inverse functions and f' is continuous,
prove that
) dx = bf(b) – af (a) – S g(v) dy
%3D
Jf (a)
[Hint: Use part (a) and make the substitution y = f(x).]
(c) In the case where f and g are positive functions and
b > a > 0, draw a diagram to give a geometric interpre-
tation of part (b).
(d) Use part (b) to evaluate In x dx.
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