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Unformatted text preview: e bottom. What do you do if the denominator is not of lower degree than the numerator?
In a word: “DIVIDE” That is, you divide the denominator into the numerator using good old
fashioned Long Division - of course now we're dividing Polynomials and not numbers but it works
the same way, using “of lower degree than” instead of “less than”. 2 To integrate: a dx First write our fraction as a long division:
Now a goes into
, 2 times so we put 2 above the
then we multiply
so this goes under the
We subtract and get
which is of lower degree (in ) than
a 2 so it's the remainder
2 and our integral becomes NOW, we can do the second integral with partial fractions multiply by the denominator a a:
let now let : 2 and our integral now becomes ln
ln ln Homework:
Find the integrals
1) 4) 7) 2) 5) 8) 3) 6) 9) Likely answers: 1) ln
; 7) ln ; 2) ln
; 8) ln ; 3) ln
; 9) ln ; 4) ln ; 5) ln ;...
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This document was uploaded on 03/24/2014 for the course CALC 2 at Northeastern.
- Fall '13