Explanation Given information: The function f ( t ) = cos t + sin t where − π ≤ t ≤ 0 . Formula used: The average of the function f ( t ) where a ≤ t ≤ b is 1 b − a ( ∫ a b f ( t ) d t ) . ∫ sin x d x = − cos x + C ∫ cos x d x = sin x + C , where C is the constant of integration. Calculation: The average of the function f ( t ) = cos t + sin t where − π ≤ t ≤ 0 is 1 0 − ( − π ) ( ∫ − π 0 ( cos t + sin t ) d t )

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 8, Problem 74RE

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To calculate: Theaverage of the function f(t)=cost+sint where −π≤t≤0.

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Chapter 8, Problem 73RE

Chapter 8, Problem 75RE

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Chapter 8 Solutions

Calculus & Its Applications (14th Edition)

Ch. 8.1 - A right triangle has one angle of /3 radians. What...Ch. 8.1 - Prob. 2CYU Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Give the radian measure of each angle described.Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.2 - Find cost, where t is the radian measure of the...Ch. 8.2 - Prob. 2CYU Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - In Exercises 112, give the values of sint and...Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - In any given locality, the length of daylight...Ch. 8.3 - Differentiate y=2sin[t2+(/6)].Ch. 8.3 - Prob. 2CYU Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Differentiate (with respect to t or x): y=2cos3t Ch. 8.3 - Differentiate (with respect to t or x): y=sin3t3 Ch. 8.3 - Prob. 7E Ch. 8.3 - Differentiate (with respect to t or x): y=tcost Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Differentiate (with respect to t or x): y=cos3t Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - 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Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8 - Explain the radian measure of an angle.Ch. 8 - Prob. 2CCE Ch. 8 - Prob. 3CCE Ch. 8 - Prob. 4CCE Ch. 8 - Prob. 5CCE Ch. 8 - Prob. 6CCE Ch. 8 - Prob. 7CCE Ch. 8 - Prob. 8CCE Ch. 8 - Prob. 9CCE Ch. 8 - Prob. 10CCE Ch. 8 - Prob. 1RE Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - Prob. 5RE Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - Prob. 16RE Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - Prob. 32RE Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Differentiate (with respect to t or x): y=ln(cosx)Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Prob. 44RE Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE Ch. 8 - Prob. 59RE Ch. 8 - Prob. 60RE Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 65RE Ch. 8 - Prob. 66RE Ch. 8 - Prob. 67RE Ch. 8 - In Fig. 2: Find the Shaded area A2.Ch. 8 - Prob. 69RE Ch. 8 - Prob. 70RE Ch. 8 - Prob. 71RE Ch. 8 - Prob. 72RE Ch. 8 - 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[ Hint: Use identity...Ch. 8 - Prob. 78RE Ch. 8 - Prob. 79RE Ch. 8 - Prob. 80RE

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Theaverage of the function f ( t ) = cos t + sin t where − π ≤ t ≤ 0 .

Solution Summary: The author calculates the average of the function f(t)=mathrmcost+

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To calculate: Theaverage of the function f(t)=cost+sint where −π≤t≤0.

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Chapter 8 Solutions