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 is exist and finite, then it is 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 ∞ 50 e − 50 x d x . The integrand f ( x ) = 50 e − 50 x is finite on the unbounded interval [ 0 , ∞ ) . Find the limit of the given improper integral to check whether it is convergent or divergent

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

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Chapter 16.4, Problem 14E

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To find: The value of the improper integral ∫0∞50e−50xdx , if it is convergent.

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Chapter 16.4, Problem 13E

Chapter 16.4, Problem 15E

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Chapter 16 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

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The value of the improper integral ∫ 0 ∞ 50 e − 50 x d x , if it is convergent.

Solution Summary: The author explains that the improper integral is convergent and its value is 1.

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To find: The value of the improper integral ∫0∞50e−50xdx , if it is convergent.

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Chapter 16 Solutions