Explanation Given: ∫ sin 5 θ cos 3 θ d θ Calculation: The given integral is ∫ sin 5 θ cos 3 θ d θ Rewrite this integral in the form of cosine function only ∫ sin θ ⋅ sin 4 θ cos 3 θ d θ = ∫ sin θ ⋅ ( 1 − cos 2 θ ) 2 cos 3 θ d θ Apply the u -substitution u = cos θ ⇒ d u = − sin θ d θ Thus, the integral becomes ∫ − u 3 ( 1 − u 2 ) 2 d

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8, Problem 29CRE

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Evaluate the integral using the appropriate method or combination of methods.

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Chapter 8, Problem 28CRE

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Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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Evaluate the integral using the appropriate method or combination of methods.

Solution Summary: The author evaluates the integral using the appropriate method or combination of methods.

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Evaluate the integral using the appropriate method or combination of methods.

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