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9. Consider the indefinite integral sin³ (x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin² (x) + cos² (x) = 1. By observing that sin³(x) = sin(x) · sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx. e. Use a similar approach to evaluate cos³(x) dx.

9. Consider the indefinite integral sin³ (x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin² (x) + cos² (x) = 1. By observing that sin³(x) = sin(x) · sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx. e. Use a similar approach to evaluate cos³(x) dx.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.3: Applications Of Systems Of Linear Equations
Problem 13E: Use sin0=0, sin2=1, and sin=0 to estimate sin3.
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9. Consider the indefinite integral ſ sin³(x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin²(x) + cos²(x) = 1. By observing that sin³(x) = sin(x) sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx. e. Use a similar approach to evaluate ſcos³(x) dx.
Transcribed Image Text:9. Consider the indefinite integral ſ sin³(x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin²(x) + cos²(x) = 1. By observing that sin³(x) = sin(x) sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx. e. Use a similar approach to evaluate ſcos³(x) dx.
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