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 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 elimination of the drug is given by R ( t ) = 3 e − 0.1 t − 3 e − 0.3 t . In order to find the amount of the drug that eliminated from the body, it is enough to integrate the expression R ( t ) = 3 e − 0.1 t − 3 e − 0.3 t over the interval [ 0 , ∞ ) . That is ∫ 0 ∞ ( 3 e − 0.1 t − 3 e − 0.3 t ) d t and simplify it by using above definition and theorem. Amount of drug eliminated from body = ∫ 0 ∞ ( 3 e − 0.1 t − 3 e − 0.3 t ) d t = 3 lim b → ∞ ∫ 0 b e − 0

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Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Differential Equations

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Chapter 11 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

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 amount of the drug that is eliminated from the body.

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