Explanation Given Information: The expression is provided as, ∫ 1 ∞ 1 x 3 d x From the definition of improper integral. ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x Also, the expression for the integration of a polynomial is as follows: ∫ x n d x = x n + 1 n + 1 + C : where n ≠ 0 . The improper integral converges if the limit exists otherwise the improper integral diverges. Consider the provided expression, ∫ 1 ∞ 1 x 3 d x Use the property of improper integral and simplify as: ∫ 1 ∞

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.4, Problem 8E

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Whether the improper integral ∫1∞1x3dx diverges or converges and to evaluate the integral if it converges.

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Chapter 6.4, Problem 7E

Chapter 6.4, Problem 9E

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Chapter 6 Solutions

Calculus: An Applied Approach (MindTap Course List)

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Whether the improper integral ∫ 1 ∞ 1 x 3 d x diverges or converges and to evaluate the integral if it converges.

Solution Summary: The author explains that the improper integral diverges as the value of integration is infty .

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Whether the improper integral ∫1∞1x3dx diverges or converges and to evaluate the integral if it converges.

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Chapter 6 Solutions