Explanation Given information: ∫ 0 4 cos x d x Calculation: The definite integral is: ∫ 0 4 cos x d x = ( ∗ ) 2 ∫ 0 2 t cos t d t = 2 ( t sin t + cos t ) | 0 2 = 2 ( 2 sin 2 + cos 2 − 1 ) = 0.8049 Integration by substitution x = t 2 ⇒ d x = 2 t d t x = 0 ⇒ t = 0 x = 4 ⇒ t = 2 ∫ 0 4 cos x d x = ∫ 0 2 cos t ⋅ 2 t d t = 2 ∫ 0 2 t cos t d t

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 5.3, Problem 36P

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Compute the definite integral ∫04cosx dx and interpret the result in terms of areas.

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Chapter 5.3, Problem 35P

Chapter 5.3, Problem 37P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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Compute the definite integral ∫ 0 4 cos x d x and interpret the result in terms of areas.

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Compute the definite integral ∫04cosx dx and interpret the result in terms of areas.

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Chapter 5 Solutions