Let f be continuous and have an inverse. Write F as the antiderivative of f, i.e., F(x) S ƒ (x)dx. Use the partial integral and substitution y = f¯'(x)to show that (2) dæ = xf=(#) – | f(4) dy = xf=1(x) – F(f¯'(x)). %3D - %3D

Calculus: Early Transcendentals
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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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Let f be continuous and have an inverse. Write F as the antiderivative of f, i.e., F(x) S ƒ (x)dx. Use the
partial integral and substitution y =ƒ-1(x)to show that
(x) dr = af(x) – | f(y) dy = xf-"(#) – F(f¯'(x)).
%3D
Transcribed Image Text:Let f be continuous and have an inverse. Write F as the antiderivative of f, i.e., F(x) S ƒ (x)dx. Use the partial integral and substitution y =ƒ-1(x)to show that (x) dr = af(x) – | f(y) dy = xf-"(#) – F(f¯'(x)). %3D
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