Explanation Definition used: Improper integral: “If f is continuous on ( − ∞ , b ] , then ∫ − ∞ b f ( x ) d x = lim a → − ∞ ∫ 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 ∫ − ∞ − 10 x − 2 d x . The integrand f ( x ) = 1 x 2 is finite on the unbounded interval ( − ∞ , − 10 ] . Find the limit of the given improper integral to check whether it is convergent or divergent

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ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

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Chapter 16.4, Problem 9E

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To find: The value of the improper integral ∫−∞−10x−2dx , if it is convergent.

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Chapter 16.4, Problem 8E

Chapter 16.4, Problem 10E

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The value of the improper integral ∫ − ∞ − 10 x − 2 d x , if it is convergent.

Solution Summary: The author explains that the improper integral is convergent and its value is 110.

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To find: The value of the improper integral ∫−∞−10x−2dx , if it is convergent.

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Chapter 16 Solutions