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Simple linear factors Evaluate the following integrals.

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 9E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 9E

Simple linear factors Evaluate the following integrals.

\(\int \frac{d x}{(x-1)(x+2)}\)

Step-by-Step Solution:

Step 1 of 3

Proper fraction definition ; In a rational fraction  , if the degree of f(x) < the degree of g(x) , then the rational fraction is called a proper fraction.

         The sum of two proper fractions is a proper fraction.

                                  Example;

Partial fractions Depending upon the nature of factors of Denominator ;

1) When the denominator has non-repeated linear factors;

                             A non - repeated linear factor (x-a) of denominator corresponds a partial fraction of the form  , where A is a constant to be determined’

                 

      If g(x) = (x-a)(x-b)(x-c)............(x-n), then we assume that

                       =  ++ +...............+

Where A, B, C,............N are constants which can be determined by equating the numerator of L.H.Sto the numerator of R.H.S , and substituting x = a,b ,c ….n.

 

Step 2 of 3

Chapter 7.4, Problem 9E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Simple linear factors Evaluate the following integrals.