Explanation Given: The provided improper integral is ∫ 2 ∞ 1 x ( ln x ) 2 d x . Calculation: Consider the provided improper integral, ∫ 2 ∞ 1 x ( ln x ) 2 d x Use the definition of improper integral to write above integral as, ∫ 2 ∞ 1 x ( ln x ) 2 d x = lim b → ∞ ∫ 2 b 1 x ( ln x ) 2 d x Now, use the fundamental theorem of calculus for the value of ∫ 2 b 1 x ( ln x ) 2 d x . ∫ 2 b 1 x ( ln x ) 2 d x = ∫ 2 b 1 ( ln x ) 2 ⋅ 1 x d x = ∫ ln 2 ln b 1 t 2 d t

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ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 8.4, Problem 24E

To determine

To find:

The value of provided improper integral ∫2∞1x(lnx)2dx and also determine the improper integral is converges or diverges.

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Chapter 8.4, Problem 23E

Chapter 8.4, Problem 25E

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Calculus For The Life Sciences

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

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The value of provided improper integral ∫ 2 ∞ 1 x ( ln x ) 2 d x and also determine the improper integral is converges or diverges.

Solution Summary: The author analyzes the value of provided improper integral and determines whether it is converges or diverges.

Concept explainers

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To find:

The value of provided improper integral ∫2∞1x(lnx)2dx and also determine the improper integral is converges or diverges.

Want to see the full answer?

Chapter 8 Solutions

The value of provided improper integral ∫ 2 ∞ 1 x ( ln x ) 2 d x and also determine the improper integral is converges or diverges.

Solution Summary: The author analyzes the value of provided improper integral and determines whether it is converges or diverges.

Concept explainers

Videos

To find: The value of provided improper integral ∫2∞1x(lnx)2dx and also determine the improper integral is converges or diverges.

Want to see the full answer?

Chapter 8 Solutions

To find:

The value of provided improper integral ∫2∞1x(lnx)2dx and also determine the improper integral is converges or diverges.