Explanation Given Information: The provided integral is ∫ 3 ( x 5 − 2 x ) ( x 6 − 6 x 2 + 7 ) − 2 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, ∫ 3 ( x 5 − 2 x ) ( x 6 − 6 x 2 + 7 ) − 2 d x Rewrite the integral by multiplying and dividing by 2 as, 1 2 ∫ ( 6 x 5 − 12 x ) ( x 6 − 6 x 2 + 7 ) − 2 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 6 − 6 x 2 + 7 and n = − 2 Differentiate u = x 6 − 6 x 2 + 7 with respect to x and get, d u = ( 6 x 5 − 12 x ) d x Now, all required parts are present, so the integral is of the form, 1 2 ∫ ( 6 x 5 − 12 x ) ( x 6 − 6 x 2 + 7 ) − 2 d x = 1 2 ∫ u − 2 d u = 1 2 ( − u − 1

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 22E

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To calculate: The value of the integral ∫3(x5−2x)(x6−6x2+7)−2dx and also check the solution by differentiation.

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Chapter 12.2, Problem 21E

Chapter 12.2, Problem 23E

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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 ∫ 3 ( x 5 − 2 x ) ( x 6 − 6 x 2 + 7 ) − 2 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 ∫3(x5−2x)(x6−6x2+7)−2dx and also check the solution by differentiation.

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Chapter 12 Solutions