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MathGroup Archive 1999

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Re: Solving difficult integral a follow up

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18665] Re: [mg18620] Solving difficult integral a follow up
  • From: Richard Gass <gass at physics.uc.edu>
  • Date: Thu, 15 Jul 1999 01:45:51 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Christian wrote
<I've got the following problem:

<I need to solve the following integral:

<Integrate[Sqrt[C0+C1*x+C2*x^2+C3*x^3+C4*x^4],{x,0,t}]

<For those of you who do not recognize it at once: it's the integral of the
<square root of a 4th degree polynomial in x. I've tried to solve the above
<integral with Mathematica, but after, say, two hours of computing I stopped
<the calculation - it looked like the Kernel crashed or whatever. Is there an
<analytical solution to this problem at all?

I replied that I could do the indefinite integral but that I thought the
definite integral was hopeless because of branch cut problems. However
my machine ( a fairly old Power Mac) run 4.0  returns an answer for
Integrate[Sqrt[C0 + C1*x + C2*x^2 + C3*x^3 + C4*x^4], {x, 0, t}]. THe
result takes a  few minutes or so. I am not at all sure the result is
correct.
Richard Gass
Department of Physics
University of Cincinnati
Cincinnati, OH 45221
phone- 513-556-0519
E-Mail gass at physics.uc.edu


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