(Never Mind? Can't duplicate result!) Re: Can

• To: mathgroup at smc.vnet.net
• Subject: [mg81880] (Never Mind? Can't duplicate result!) Re: [mg81827] Can
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Fri, 5 Oct 2007 04:59:30 -0400 (EDT)
• References: <200710040827.EAA22349@smc.vnet.net>

```Dear Mathgroup,
I've tried again to duplicate the results below with a fresh
kernal, and I can't. I am now getting a sensible result.

Apologies to anyone who might have put time into this.

Craig

On Thu, 4 Oct 2007, W. Craig Carter wrote:

> Date: Thu, 4 Oct 2007 04:27:21 -0400 (EDT)
> From: W. Craig Carter <ccarter at MIT.EDU>
> To: mathgroup at smc.vnet.net
> Subject: [mg81827] Can Integrate[expr,{x,a,b}] give an incorrect result?
>
>
> I believe I am getting an incorrect result from a definite
> integration:
>
> InputForm[integrand] is
> (R*(R - rho*Cos[alpha - t]))/(3*(R^2 + rho^2 + (z - zeta)^2 - 2*R*rho*Cos[alpha - t])^3)
>
> InputForm[assumptions] is
> {R > 0, L > 0, rho > 0, Element[zeta, Reals], Element[z, Reals], alpha > 0}
>
> Integrate[integrand,{t,0,2Pi},Assumptions->assumptions]
> returns 0
>
> But compare this to:
> (visually integrate...)
> Plot[integrand/.{R -> 1, rho -> 1.1, zeta -> 0, alpha -> 0, z -> 1.2},{t,0,2 Pi},PlotRange->All]
>
> (numerically integrate...)
> Plot[NIntegrate[integrand/.{{R -> 1, rho -> 1.1, zeta -> 0, alpha -> 0, z -> 1.2},{t,0,tau}],{tau,0,2Pi}, PlotRange->All]
>
>