Question

a) Use partial fraction decomposition to write frac{4x-8}{x^2-16} as the sum of two partial fractions. b) Use the decomposition from part (a) to evaluate int frac{4x-8}{x^2-16} dx.

          a) Use partial fraction decomposition to write frac{4x-8}{x^2-16} as the sum of two partial fractions.
b) Use the decomposition from part (a) to evaluate int frac{4x-8}{x^2-16} dx.

$a) Use partial fraction decomposition to write frac4x-8x^2-16 as the sum of two partial fractions. b) Use the decomposition from part (a) to evaluate int frac4x-8x^2-16 dx.$

Added by Nuria W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

05/27/2022

Step 1

Given expression: $\frac{4x - 8}{x^2 - 16}$ We can express the denominator $x^2 - 16$ as $(x + 4)(x - 4)$. So, we can write the given expression as: $\frac{4x - 8}{x^2 - 16} = \frac{A}{x + 4} + \frac{B}{x - 4}$ Show more…

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a) Use partial fraction decomposition to write (4x - 8) / (x^2 - 16) as the sum of two partial fractions. b) Use the decomposition from part (a) to evaluate integral of (4x - 8) / (x^2 - 16) dx.