Explanation Formula used: Trigonometric identity: 1 + tan 2 x = sec 2 x Derivative of the secant function: d d x ( sec a x ) = a sec a x tan a x Calculation: The given integral is ∫ tan 3 3 θ sec 3 3 θ d θ . The integral ∫ tan 3 3 θ sec 3 3 θ d θ can be written as follows, ∫ tan 3 3 θ sec 3 3 θ d θ = ∫ tan 2 3 θ sec 2 3 θ tan 3 θ sec 3 θ d θ = ∫ ( sec 2 3 θ − 1 ) sec 2 3 θ tan 3 θ sec 3 θ d θ [ ∵ 1 + tan 2 x = sec 2 x ] Let u = sec 3 θ and d u = 3 tan 3 θ sec 3 θ d θ . Substitute u = sec 3 θ and d u 3 = tan 3 θ sec 3 θ d θ in ∫ tan 3 3 θ sec 3 3 θ d θ , ∫ tan 3 3 θ sec 3 3 θ d θ

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

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ISBN: 9780135243435

Author: Bill Briggs

Publisher: Pearson Education (US)

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Chapter 8, Problem 33RE

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To evaluate: The integral ∫tan33θsec33θdθ based on integration by parts.

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Chapter 8, Problem 32RE

Chapter 8, Problem 34RE

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MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

Ch. 8.1 - What change of variable would you use for the...Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - What change of variables would you use for the...Ch. 8.1 - Prob. 2E Ch. 8.1 - What trigonometric identity is useful in...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E

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The integral ∫ tan 3 3 θ sec 3 3 θ d θ based on integration by parts.

Solution Summary: The author explains how the integral displaystyle is evaluated based on integration by parts.

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To evaluate: The integral ∫tan33θsec33θdθ based on integration by parts.

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Chapter 8 Solutions