Explanation Given: Formula used: ∫ [ f ( u ) ± g ( u ) ] d u = ∫ f ( u ) d u ± ∫ g ( u ) d u Calculation: Consider the given function. y = 124 p ( 10 + p ) ( 100 − p ) Average cost of removing p % of chemical from waste water is 1 80 − 75 ∫ 75 80 124 p ( 10 + p ) ( 100 − p ) d p Now, ∫ 124 p ( 10 + p ) ( 100 − p ) d p = 124 ∫ p ( 10 + p ) ( 100 − p ) d p Include one partial fraction for each factor and write p ( 10 + p ) ( 100 − p ) = A 10 + p + B 100 − p Multiplying this equation with the least common denominator, we get p = A ( 100 − p ) + B ( 10 + p ) Because this equation is true for all p , we can substitute any convenient value for p to find A and B . To solve for A , let p = − 10 . A ( 100 + 10 ) + B ( 10 − 10 ) = − 10 110 A = − 10 A = − 1 11 To solve for B , let p = 100 . A ( 100 − 100 ) + B ( 10 + 100 ) = 100 110 B = 100 B = 10 11 So, the decomposition is p ( 10 + p ) ( 100 − p ) = − 1 11 10 + p + 10 11 100 − p = − 1 11 ( 10 + p ) + 10 11 ( 100 − p ) = − 1 11 ( p + 10 ) − 10 11 ( p − 100 ) Thus, ∫ 124 p ( 10 + p ) ( 100 − p ) d p = 124 ∫ ( − 1 11 ( p + 10 ) − 10 11 ( p − 100 ) ) d p Use the basic integration rule: ∫ [ f ( u ) ± g ( u ) ]

Calculus: Early Transcendental Functions (MindTap Course List)

6th Edition

ISBN: 9781285774770

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.5, Problem 45E

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Chapter 8.5, Problem 44E

Chapter 8.5, Problem 46E

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Calculus: Early Transcendental Functions (MindTap Course List)

Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 14, select...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, selectthe...

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The average cost of removal of 75 % to 80 % of chemical.

Solution Summary: The author calculates the average cost of removing p% of chemical from waste water.

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