Explanation Calculation: Rewrite the given function 8 ( x 2 + 4 ) x ( x 2 + 8 ) using method of partial fraction, 8 ( x 2 + 4 ) x ( x 2 + 8 ) = A x + B x + C x 2 + 8 (1) Multiply both sides of equation (1) by x ( x 2 + 8 ) , A ( x 2 + 8 ) + B x 2 + C x = 8 ( x 2 + 4 ) (2) Substitute x = 0 in equation (2), A ( ( 0 ) 2 + 8 ) + B ( 0 ) 2 + C ( 0 ) = 8 ( ( 0 ) 2 + 4 ) 8 A = 32 A = 4 Thus, the value A = 4 . Substitute x = 1 in equation (2), A ( ( 1 ) 2 + 8 ) + B ( 1 ) 2 + C ( 1 ) = 8 ( ( 1 ) 2 + 4 ) 9 A + B + C = 40 9 ( 4 ) + B + C = 40 B + C = 4 Thus, the value of B + C = 4 (3) Substitute x = − 1 in equation (2), A ( ( − 1 ) 2 + 8 ) + B ( − 1 ) 2 + C ( − 1 ) = 8 ( ( − 1 ) 2 + 4 ) 9 A + B − C = 40 9 ( 4 ) + B − C = 40 ( ∵ A = 4 ) B − C = 4 Thus, the value of B − C = 4 (4) Add the equation (3) and (4), B + C + B − C = 4 + 4 2 B = 8 B = 4 Thus, the value of B = 4

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 7.5, Problem 42E

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To evaluate: The integral ∫8(x2+4)x(x2+8)dx.

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Chapter 7.5, Problem 41E

Chapter 7.5, Problem 43E

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Chapter 7 Solutions

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

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The integral ∫ 8 ( x 2 + 4 ) x ( x 2 + 8 ) d x .

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To evaluate: The integral ∫8(x2+4)x(x2+8)dx.

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Chapter 7 Solutions