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Calculus for Biology Class Notes Partial Fractions

What do you do if the denominator is not of lower

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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 2 So 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 6) ln ; 7) ln ; 2) ln ; 8) ln ; 3) ln ; 9) ln ; 4) ln ; 5) ln ;...
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