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