Explanation Given Information: The total value of a continuous income stream R ( t ) dollars per year from time a to b is, ∫ a b R ( t ) d t . Formula Used: The total income received from x = a to x = b is, ∫ a b f ( x ) d x , where function f ( x ) is the income stream. The sum and difference rules for an integral is, ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x , where f ( x ) and g ( x ) are two functions. If the function is f ( x ) = sin ( a x + b ) , and a and b are constants, with a ≠ 0 then the formula for the integration of the function is given by ∫ sin ( a x + b ) d x = − 1 a x + b cos ( a x + b ) + C . Constant multiple rule is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. Calculation: Consider the provided function, R ( t ) = 50 , 000 + 2 , 000 π sin ( 2 π t ) . Determine the total income received ∫ a b R ( t ) d t for limit 0 ≤ t ≤ 1 , T V = ∫ 0 1 ( 50 , 000 + 2 , 000 π sin ( 2 π t ) ) d t To evaluate the integral R ( t ) = ∫ 0 1 ( 50 , 000 + 2 , 000 π sin ( 2 π t ) ) d t , suppose that the function f ( u ) is ∫ 0 1 ( 50 , 000 ) d t and g ( u ) is ∫ 0 1 ( 2 , 000 π sin ( 2 π t ) ) d t

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 16.3, Problem 69E

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To calculate: The total value of the income stream $R(t)=50,000+2,000πsin(2πt)$ over the period $0≤t≤1$ .

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Chapter 16.3, Problem 68E

Chapter 16.3, Problem 70E

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Chapter 16 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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The total value of the income stream R ( t ) = 50 , 000 + 2 , 000 π sin ( 2 π t ) over the period 0 ≤ t ≤ 1 .

Solution Summary: The author calculates the total value of the income stream R(t)=50,000+2,000pi mathrmsin

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To calculate: The total value of the income stream $R(t)=50,000+2,000πsin(2πt)$ over the period $0≤t≤1$ .

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Chapter 16 Solutions