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# 7.4 Integration of Rational Functions by Partial Fractions .. 7.4 Integration of Rational Functions by Partial Fractions Question #2 (Medium)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
7.4 Integration Techniques Partial Fractions for Rational Functions Question #2 (Medium): Evaluating the Definite Integral Using Partial Fractions Strategy 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. Sample Question Evaluate the definite integral using partial fractions. ∫ ( ) ( ) Solution Since the denominator is already factored, coefficients need to be determined to evaluate the integral. So, ( ) ( ) ( ) ( ) ( ). Since ( ) is of order 2, it needs to be written twice. Then the numerators are written as: ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
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