Explanation Given Information: The provided integral is, ∫ 0 ∞ x 2 e − x 3 d x Formula used: According to the exponential rule of integrals, ∫ e x d x = e x + C If the limit defining the improper integral is a unique finite number, then integral converges else it diverges, ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x Calculation: Consider the provided integral, ∫ 0 ∞ x 2 e − x 3 d x Now, use the formula, ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x Also, multiply and divide the integral by − 3 and rewrite as, ∫ 0 ∞ x 2 e − x 3 d x = − 1 3 lim b → ∞ ∫ 0 b − 3 x 2 e − x 3 d x Now, let − x 3 = t , Differentiate both the sides, − 3 x 2 d x = d t Therefore, the integral becomes, ∫ 0 ∞ x 2 e −

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 13.7, Problem 6E

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To calculate: The value of the improper integral ∫0∞x2e−x3dx if it converges.

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Chapter 13.7, Problem 5E

Chapter 13.7, Problem 7E

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Chapter 13 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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The value of the improper integral ∫ 0 ∞ x 2 e − x 3 d x if it converges.

Solution Summary: The author calculates the value of the provided integral, 13 if it converges.

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To calculate: The value of the improper integral ∫0∞x2e−x3dx if it converges.

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Chapter 13 Solutions