Explanation Given information: Given integral is ∫ 4 x ( x 2 + 1 ) d x Calculation: Consider the integral ∫ 4 x ( x 2 + 1 ) d x Simplifying, ∫ 4 x ( x 2 + 1 ) d x = ∫ ( 4 x ( x 2 ) + 4 x ( 1 ) ) d x ∫ 4 x ( x 2 + 1 ) d x = ∫ ( 4 x 3 + 4 x ) d x Distributing the integral and then simplifying, ∫ 4 x ( x 2 + 1 ) d x = ∫ 4 x 3 d x + ∫ 4 x d x x To determine (b) To calculate the given integral using substitution. To determine (c) To explain: To explain how the expressionsfrom parts (a) and (b)are different and to check if both are correct.

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 6.6, Problem 66P

To determine

(a)

To calculate the given integral by multiplying first and then using antiderivative.

To determine

(b)

To calculate the given integral using substitution.

To determine

(c)

To explain:

To explain how the expressionsfrom parts (a) and (b)are different and to check if both are correct.

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Chapter 6.6, Problem 65P

Chapter 6.6, Problem 67P

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Chapter 6 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

Ch. 6.1 - Prob. 1P Ch. 6.1 - Prob. 2P Ch. 6.1 - Prob. 3P Ch. 6.1 - Prob. 4P Ch. 6.1 - Prob. 5P Ch. 6.1 - Prob. 6P Ch. 6.1 - Prob. 7P Ch. 6.1 - Prob. 8P Ch. 6.1 - Prob. 9P Ch. 6.1 - Prob. 10P

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(a) To calculate the given integral by multiplying first and then using antiderivative.

Solution Summary: The author calculates the given integral by multiplying first and then using antiderivative.

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(a) To calculate the given integral by multiplying first and then using antiderivative.

(b) To calculate the given integral using substitution.

(c) To explain: To explain how the expressionsfrom parts (a) and (b)are different and to check if both are correct.

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Chapter 6 Solutions

(a)

To calculate the given integral by multiplying first and then using antiderivative.

(b)

To calculate the given integral using substitution.

(c)

To explain:

To explain how the expressionsfrom parts (a) and (b)are different and to check if both are correct.