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EXAMPLE 3 Evaluate SOLUTION If we write sin2(9x) = 1 – cos?(9x), the integral is no simpler to %3D evaluate. Using the half-angle formula for sin2(x), however, we have IT sin2(9x) dx (1 – cos(18x)) dx %3D - {(-[ IT ] )-o-[ Notice that we mentally made the substitution u = 18x when integrating cos(18x). Another method for evaluating this integral was given in this exercise. II

EXAMPLE 3 Evaluate SOLUTION If we write sin2(9x) = 1 – cos?(9x), the integral is no simpler to %3D evaluate. Using the half-angle formula for sin2(x), however, we have IT sin2(9x) dx (1 – cos(18x)) dx %3D - {(-[ IT ] )-o-[ Notice that we mentally made the substitution u = 18x when integrating cos(18x). Another method for evaluating this integral was given in this exercise. II

Calculus: Early Transcendentals
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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EXAMPLE 3 Evaluate sin?(9x) dx. SOLUTION If we write sin?(9x) = 1 – cos²(9x), the integral is no simpler to evaluate. Using the half-angle formula for sin2(x), however, we have sin?(9x) dx 2 1 (1 – cos(18x)) dx - {-[ - {(- - )- {0 - Notice that we mentally made the substitution u = 18x when integrating cos(18x). Another method for evaluating this integral was given in this exercise.
Transcribed Image Text:EXAMPLE 3 Evaluate sin?(9x) dx. SOLUTION If we write sin?(9x) = 1 – cos²(9x), the integral is no simpler to evaluate. Using the half-angle formula for sin2(x), however, we have sin?(9x) dx 2 1 (1 – cos(18x)) dx - {-[ - {(- - )- {0 - Notice that we mentally made the substitution u = 18x when integrating cos(18x). Another method for evaluating this integral was given in this exercise.
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