(a) 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, ∫ 8 ∞ 1 x 1 3 d x . Find the limit of the given improper integral to check whether it is convergent or divergent (b) To determine To find: The value of the improper integral ∫ 8 ∞ 1 x 4 3 d x , if it is convergent.

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 16.4, Problem 1YT

(a)

To determine

To find: The value of the improper integral ∫8∞1x13dx , if it is convergent.

(b)

To determine

To find: The value of the improper integral ∫8∞1x43dx , if it is convergent.

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Chapter 16.3, Problem 20E

Chapter 16.4, Problem 2YT

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Chapter 16 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

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The value of the improper integral ∫ 8 ∞ 1 x 1 3 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 ∫8∞1x13dx , if it is convergent.

To find: The value of the improper integral ∫8∞1x43dx , if it is convergent.

Want to see the full answer?

Chapter 16 Solutions