Explanation Given information: Breathing is cyclic and one respiratory cycle takes about 5 seconds. Calculation: Breathing is cyclic and one respiratory cycle takes about 5 seconds. The rate of air flow into the lungs f t = 1 2 sin 2 π t 5 The volume of inhaled air into the lungs at time t V = ∫ 0 t f t d t = 1 2 ∫ 0 t sin 2 π t 5 d t Let 2 π t 5 = x ⇒ 2 π 5 d t = d x ⇔ d t = 5 2 π d x When t = 0 , x = 0 V = 5 4 π − cos x 0 2 π t 5 = 5 4 π − cos 2 π t 5 + cos 0 V = 5 4 π 1 − cos 2 π t 5 [ in units of liters ] The time interval 0 , 5 for one respiratory cycle, where a = 0 and b = 5 The average volume of air in one cycle V a v g = 1 b − a ∫ a b V t = 1 5 − 0 ∫ 0 5 5 4 π 1 − cos 2 π t 5 d t The time interval 0 , 5 for one respiratory cycle, where a = 0 and b = 5

Calculus: Early Transcendentals, Loose-leaf Version, 9th

9th Edition

ISBN: 9780357022290

Author: Stewart

Publisher: Cengage Learning Acquisitions

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Chapter 6.5, Problem 23E

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To find: Average volume of inhaled sir in the lungs in one respiratory cycle.

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Chapter 6.5, Problem 22E

Chapter 6.5, Problem 24E

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Chapter 6 Solutions

Calculus: Early Transcendentals, Loose-leaf Version, 9th

Ch. 6.1 - (a) Set up an integral for the area of the shaded...Ch. 6.1 - (a) Set up an integral for the area of the shaded...Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region. 5.Ch. 6.1 - Find the area of the shaded region. 6.Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Prob. 8E Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Set up, but do not evaluate, an integral...

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Average volume of inhaled sir in the lungs in one respiratory cycle.

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