Partial Fraction Notes

# Partial Fraction Notes - Example 0.2 Determine the...

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Partial Fractions (Section 7.4) The method of partial fractions is used to evaluate integrals of the form Z p ( x ) q ( x ) dx where p ( x ) and q ( x ) are polynomials. Polynomial Long Division Review: Example 0.1. x 2 + 5 x + 9 Rule 1: Evaluating Z p ( x ) q ( x ) where q ( x ) is the product of linear factors, none of which is repeated, so q ( x ) = ( a 1 x + b 1 )( a 2 x + b 2 ) ... ( a n x + b n ): 1. If the degree of p ( x ) is greater than the degree of q ( x ), long divide ﬁrst. 2. Write p ( x ) q ( x ) = A 1 a 1 x + b 1 + A 2 a 2 x + b 2 + ... + A n a n x + b n 3. Clear denominators from both sides. 4. Use coeﬃcient matching to set up a system of n equations with n unknowns. 5. Use your favorite method to solve the system of equations.

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Unformatted text preview: Example 0.2. Determine the coeﬃcient of the 1 x + 2 term in the partial fraction decomposition of-x-4 x 2-2 x-8 . Example 0.3. Determine the coeﬃcient on the x term in the partial fraction decom-position of 3 x 3 + 5 x 2 x 2-2 x + 4 . Example 0.4. Z x 4 x 2-1 dx Example 0.5. Z x x 2 + 5 x + 6 dx Example 0.6. Z x 3 x-1 dx Example 0.7. Z x 2 + 5 x x 2-4 dx Example 0.8. Z x + 9 x 2-1 dx...
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Partial Fraction Notes - Example 0.2 Determine the...

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