MATH
Calc08_4day1

# Calc08_4day1 - 8.4 Partial Fractions The Empire Builder...

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The Empire Builder, 1957 8.4 Partial Fractions Greg Kelly, Hanford High School, Richland, Washington

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2 5 3 2 3 x dx x x - - - This would be a lot easier if we could re-write it as two separate terms. ( 29 ( 29 5 3 3 1 x x x - - + 3 1 A B x x = + - + Multiply by the common denominator. ( 29 ( 29 5 3 1 3 x A x B x - = + + - 5 3 3 x Ax A Bx B - = + + - Set like-terms equal to each other. 5 x Ax Bx = + 3 3 A B - = - 5 A B = + 3 3 A B - = - Solve two equations with two unknowns. 1
2 5 3 2 3 x dx x x - - - ( 29 ( 29 5 3 3 1 x x x - - + 3 1 A B x x = + - + ( 29 ( 29 5 3 1 3 x A x B x - = + + - 5 3 3 x Ax A Bx B - = + + - 5 x Ax Bx = + 3 3 A B - = - 5 A B = + 3 3 A B - = - Solve two equations with two unknowns. 5 A B = + 3 3 A B - = - 3 3 A B = - + 8 4 B = 2 B = 5 2 A = + 3 A = 3 2 3 1 dx x x + - + 3ln 3 2ln 1 x x C - + + + This technique is called Partial Fractions 1

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Good News! The AP Exam only requires non-repeating linear factors! The more complicated methods of partial fractions are good to know, and you might see them in college, but they will not be on the AP exam or on my exam.
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