Explanation Given Information: The provided integral is ∫ ( 2 x 3 − x ) ( x 4 − x 2 ) 6 d x . Formula used: According to the power formula of integrals, if u = u ( x ) , then, ∫ u n d u = u n + 1 n + 1 + C According to the power rule of derivative, d d x ( x n ) = n x n − 1 Calculation: Consider the provided integral, ∫ ( 2 x 3 − x ) ( x 4 − x 2 ) 6 d x Rewrite the integral by multiplying and dividing by 2 as, 1 2 ∫ 2 ( 2 x 3 − x ) ( x 4 − x 2 ) 6 d x Consider the power rule of integrals, ∫ u n d u = u n + 1 n + 1 + C Now, to use the power rule, the integrand should have the function u ( x ) and its derivative u ′ ( x ) and n ≠ − 1 . Let, u = x 4 − x 2 and n = 6 Differentiate u = x 4 − x 2 with respect to x and get, d u = 2 ( 2 x 3 − x ) d x Now, all required parts are present, so the integral is of the form, 1 2 ∫ 2 ( 2 x 3 − x ) ( x 4 − x 2 ) 6 d x = 1 2 ∫ u 6 d</

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 12.2, Problem 20E

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To calculate: The value of the integral ∫(2x3−x)(x4−x2)6dx and also check the solution by differentiation.

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Chapter 12.2, Problem 19E

Chapter 12.2, Problem 21E

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Chapter 12 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The value of the integral ∫ ( 2 x 3 − x ) ( x 4 − x 2 ) 6 d x and also check the solution by differentiation.

Solution Summary: The author calculates the value of the integral by multiplying and dividing by 2 and checking the solution by differentiation.

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To calculate: The value of the integral ∫(2x3−x)(x4−x2)6dx and also check the solution by differentiation.

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Chapter 12 Solutions