Explanation Definition used: Let f be a continuous function on the unbounded interval ( − ∞ , b ] . Then, the improper integral of f over ( − ∞ , b ] is defined by ∫ − ∞ b f ( x ) d x = lim a → − ∞ ∫ a b f ( x ) d x . If the limit exists, the improper integral is said to be convergent, otherwise divergent. Theorem used: Fundamental Theorem: “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) .” Calculation: The given improper integral is ∫ − ∞ 0 1 ( 4 x − 1 ) 3 2 d x . The integrand f ( x ) = 1 ( 4 x − 1 ) 3 2 is continuous on the unbounded interval ( − ∞ , b ] . Obtain the value of f ( x ) = 1 ( 4 x − 1 ) 3 2 . ∫ − ∞ 0 1 ( 4 x − 1 ) 3 2 d x = lim a → − ∞ ∫ a 0 1 ( 4 x − 1 ) 3 2 d x = lim a → − ∞ 1 4 [ ( 4 x − 1 ) 1 − 3 2 1 − 3 2 ] a 0 = − 2 4 lim a → − ∞ [ 1 ( 4 ( 0 ) − 1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

10th Edition

ISBN: 9781285464640

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 7.4, Problem 28E

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To check: The integral ∫−∞01(4x−1)32dx is convergent or not and compute the value of the integral if it is convergent.

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Chapter 7.4, Problem 27E

Chapter 7.4, Problem 29E

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Chapter 7 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

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Ch. 7.1 - Prob. 9E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 26E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - In Exercises 29-34, evaluate each definite...Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Find the function f given that the slope of the...Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Production of Steam Coal In keeping with the...Ch. 7.1 - Prob. 41E Ch. 7.1 - Concentration of a Drug in the Bloodstream The...Ch. 7.1 - Prob. 43E Ch. 7.1 - Average price of a Commodity The price of a...Ch. 7.1 - Distance Covered by a Car The velocity of the...Ch. 7.1 - Credit Card Losses in the United Kingdom The mail...Ch. 7.1 - U.S. Smartphone Users Smartphone users, as a...Ch. 7.1 - Prob. 49E Ch. 7.1 - Future Value of AN Investment Laura, the sole...Ch. 7.1 - Rate of Return on an Investment Suppose an...Ch. 7.1 - Present Value of A Franchise Tracy purchased a...Ch. 7.1 - Gini Index Refer to Section 6.7. 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To check: The integral ∫ − ∞ 0 1 ( 4 x − 1 ) 3 2 d x is convergent or not and compute the value of the integral if it is convergent.

Solution Summary: The author analyzes whether the integral is convergent or not, and computes the value of the improper integral.

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To check: The integral ∫−∞01(4x−1)32dx is convergent or not and compute the value of the integral if it is convergent.

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Chapter 7 Solutions