Rational Functions and Partial Fractions
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چکیده
Our final integration technique deals with the class of functions known as rational functions. Recall from Calculus I that DEFINITION 7.1. A rational function 1 is a function that is the ratio of two polynomials 1 Here 'rational' means 'ratio', as in 'the ratio of two polynomials.' r(x) = p(x) q(x) , where p(x) and q(x) are polynomials. (Remember a polynomial has the form p(x) = a n x n + a n−1 x n−1 + · · · + a 1 x + a 0 , where the a i are real constants and n is a non-negative integer and is called the degree of the polynomial.) Here are several examples of rational functions; identify the polynomials p(x) and q(x).
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