MAT136H1 Lecture Notes - Partial Fraction Decomposition, Antiderivative
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MAT136H1 Full Course Notes
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Question #2 (medium): evaluating the definite integral using partial fractions. Before evaluating the definite integral, rational function needs to be decomposed by partial fractions. Once the numerator coefficients are determined, taking the anti-derivative is easy. To decompose as much as possible, factored binomials with power greater than 1 must be written by that number of times. Since the denominator is already factored, coefficients need to be determined to evaluate the integral. Since ( ) is of order 2, it needs to be written twice. So, the numerators are written as: ( )( ) ( ) ( ) ( ) Substitute into the other equations: ( ) , so . Then through partial fraction, the integral is decomposed into:
