       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

```

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