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finisher


Advanced Newbie


Joined: 29 Apr 2007
Posts: 95

Posted: 22 Mar 2010 06:02:56 pm    Post subject:

There is this question for calculus I'm taking. It's Integral Calculus.

The question is:

"If f is a quadratic function such that f(0)=1 and integral of f(x)/( (x^2)(x+1)^3) dx is a rational function, find f'(0)
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thornahawk
μολών λαβέ


Active Member


Joined: 27 Mar 2005
Posts: 569

Posted: 22 Mar 2010 06:28:38 pm    Post subject:

First, you might want to tell us what you've already tried to solve this one.

Hint 1: Quadratics generally come in the form f(x)=ax˛+bx+c ; what is f'(0) in this case?

Hint 2: Integrating a rational function usually ends up as a linear combination of logarithms and rational functions; what does that mean for the numerator if the integral only comes up as a rational function?

thornahawk
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finisher


Advanced Newbie


Joined: 29 Apr 2007
Posts: 95

Posted: 22 Mar 2010 06:36:15 pm    Post subject:

Sorry about that D:

Well, I already deduced that any x^3 terms and x^4 terms should result in zero, meaning their co-efficients must be zero (or add up to zero). Also, the fact that f(0)=1 means that I deduced one more thing (related to partial fraction decomposition).

Answer to hint 1: f'(0) should be simply b, right?

Answer to hint 2: I'm sorry, I'm having a bit of difficulty understanding that concept Sad
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finisher


Advanced Newbie


Joined: 29 Apr 2007
Posts: 95

Posted: 22 Mar 2010 06:38:11 pm    Post subject:

Oh yea, I did this:

f(x)= A/x + B/x^2 + C/x+1 + D/(x+1)^2 + E/(x+1)^3

This is the partial fraction decomposition I did. Could you please tell me the answer to hint 2? I'm baffled.


Last edited by Guest on 22 Mar 2010 06:41:10 pm; edited 1 time in total
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