Explanation Definition used: Improper integral: “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it is converges otherwise diverges”. 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 rate of immigration into the country for t years is given by R ( t ) = 400 ( 5 + t ) 2.5 . Assume that the policy is applied indefinitely. In order to find total immigrants that comes under country policy, it enough to integrate the expression R ( t ) = 400 ( 5 + t ) 2.5 over the interval [ 0 , ∞ ) . Total immigrants = ∫ 0 ∞ 400 ( 5 + t ) 2.5 d t = 400 lim b → ∞ ∫ 0 b ( 5 + t ) − 2.5 d t = − 400 1

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Differential Equations

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Chapter 11.1, Problem 72E

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To find: The total number of immigrants.

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Chapter 11.1, Problem 71E

Chapter 11.2, Problem 1MP

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Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The total number of immigrants.

Solution Summary: The author explains that the total number of immigrants is approximately 24 million. If F is anti-derivative of f on left[a,bright], then it is converges otherwise diverges.

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Chapter 11 Solutions