Explanation Given information: R ( t ) = 50 e − t 20 is the property tax revenue at t miles from the center of a city in thousand dollars per year. Explanation: The total property tax revenue generated by property within 10 miles of the center is ∫ 0 10 2 π t ( 50 e − t 20 ) d t . Simplify. ∫ 0 10 2 π t ( 50 e − t 20 ) d t = 100 π ∫ 0 10 t e − t 20 d t Use the integration by parts rule, Let f ( t ) = t and g ( t ) = e − t 20 , then f ' ( t ) = 1 , G ( t ) = ∫ e − t 20 d t = − 20 e − t 20 And by integrating g ( t ) with respect to t , it gives Substitute values of f ( t ) , f ' ( t ) and G ( t ) in ∫ f ( x ) g ( x ) d x = f ( x ) G ( x ) − ∫ f ' ( x ) G ( x ) d x . 100 π ∫ 0 10 t e − t 20 d t = 100 π [ t ( − 20 e − t 20 ) | 0 10 − ∫ 0 10 1 ( − 20 e − t 20 ) d t ] = 100 π [ ( − 20 t e − t 20 ) | 0 10

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Chapter 9, Problem 56RE

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The total property tax revenue generated by property within 10 miles of the city center, where R(t) = 50e− t20 is the property tax revenue at t miles from the center of a city in thousand dollars per year.

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Chapter 9, Problem 55RE

Chapter 9, Problem 57RE

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The total property tax revenue generated by property within 10 miles of the city center, where R ( t ) = 50 e − t 20 is the property tax revenue at t miles from the center of a city in thousand dollars per year.

Solution Summary: The author explains that the total property tax revenue generated by property within 10 miles of the city center is 11,335 thousand.

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The total property tax revenue generated by property within 10 miles of the city center, where R(t) = 50e− t20 is the property tax revenue at t miles from the center of a city in thousand dollars per year.

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