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 ∫ − ∞ − 1 2 x − 1 x 2 − x d x . Find the limit of the given improper integral to check whether it is convergent or divergent. ∫ − ∞ − 1 2 x − 1 x 2 − x d x = lim a → − ∞ ∫ a − 1 2 x − 1 x 2 − x d x = lim a → − ∞

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Chapter 16.4, Problem 21E

To determine

To find: The value of the improper integral ∫−∞−12x−1x2−xdx , if it is convergent.

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Chapter 16.4, Problem 20E

Chapter 16.4, Problem 22E

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Chapter 16 Solutions

Finite Mathematics and Calculus with Applications

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The value of the improper integral ∫ − ∞ − 1 2 x − 1 x 2 − x d x , if it is convergent.

Solution Summary: The author explains how to find the value of the improper integral, if it is convergent or divergent.

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To find: The value of the improper integral ∫−∞−12x−1x2−xdx , if it is convergent.

Want to see the full answer?

Chapter 16 Solutions