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MathGroup Archive 1999

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Re: Re: Solving difficult integral a follow up

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18745] Re: [mg18665] Re: [mg18620] Solving difficult integral a follow up
  • From: me <me at talmanl1.mscd.edu>
  • Date: Sat, 17 Jul 1999 02:36:55 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> Date: Thu, 15 Jul 1999 01:45:51 -0400
> From: Richard Gass <gass at physics.uc.edu>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg18745] [mg18665] Re: [mg18620] Solving difficult integral a follow up
> 
> 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
> 

My Mac (a G3 that's about a year old) will do the symbolic integral, too.  It 
results in about 13 pages of Root Objects intermixed with Elliptic functions and 
Arcsins.  However, when I substitute the value 1 for each of the coefficients 
and try to plot the resulting integral over the interval from 0 to 5, 
Mathematica v4 responds with "not a machine-size real number" messages and 
produces no plot.  This in spite of the fact that 1 + x + x^2 + x^3 + x^4 is a 
positive real number everywhere.

--Lou Talman
  Department of Mathematical and Computer Sciences
  Campus Box 38
  Metropolitan State College of Denver
  PO Box 173362
  Denver CO 80217-3362

  http://clem.mscd.edu/~talmanl



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