Re: Indefinite Integrals?
- To: mathgroup at smc.vnet.net
- Subject: [mg26174] Re: Indefinite Integrals?
- From: "Paul Lutus" <nospam at nosite.com>
- Date: Thu, 30 Nov 2000 01:04:15 -0500 (EST)
- References: <8vvpvd$37r@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"drek" <drek1976 at yahoo.com> wrote in message news:8vvpvd$37r at smc.vnet.net... > Hi, > I have defined some parameters as follows: > k0:=1.52 > u0 := Sqrt[x^2 - k0^2] > u :=Sqrt[x^2 - 2.56 * k0^2] > DTE := u0 + u * Coth[u*2.0] > J0[b_] := BesselJ[0, b] > > I then try to integrate a function as follows: > GA=Integrate[J0[x * 2] * x / DTE, {x, 0, 100}] > > Errors occur as a singularity exists at DTE for x=0, resulting in indefinite > integrals. I believe that it may be possible to solve the integration > problem using the residue theorem. However, I would like to know if there > are any functions available in Mathematica 4.0 which may be able to solve > such indefinite integrals. As you may have noticed, Mathematica can produce the integral all right, the problem comes up when it tries to produce numerical results. I discovered that there are a number of singularities in your integral, so it may not be able to produce numerical results. I found them by creating a function: ff[x_] = J0[x * 2] * x / DTE; Then I used this to locate a few zeros: Table[q = FindRoot[ff[x],{x,z}],{z,0,3,.3}] // TableForm Some of the zeros are near singularities, some are simple zeros. You should also try to plot the function: Plot[ff[x],{x,0,9}] This produces some error messages, but it also plots the function and you can see why you are having problems with it. -- Paul Lutus www.arachnoid.com