MAT136H1 Lecture Notes - Partial Fraction Decomposition, Antiderivative
![](https://s3.us-east-1.wasabisys.com/prealliance-avatars.oneclass.com/avatars/515914/small/RackMultipart20201118-71849-4b6192.png?1637711045)
![MAT136H1 Full Course Notes](https://new-docs-thumbs.oneclass.com/doc_thumbnails/list_view/2418954-class-notes-ca-utsg-mat-136h1-lecture21.jpg)
92
MAT136H1 Full Course Notes
Verified Note
92 documents
Document Summary
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: