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Result Duplicated! Re: Can Integrate[expr,{x,a,b}] give

• To: mathgroup at smc.vnet.net
• Subject: [mg81849] Result Duplicated! Re: [mg81827] Can Integrate[expr,{x,a,b}] give
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Fri, 5 Oct 2007 04:43:31 -0400 (EDT)
• References: <200710040827.EAA22349@smc.vnet.net> <Pine.OSX.4.64.0710041039510.9889@pruffle.mit.edu>

I take it back. I've just duplicated the result again. I 
think this IS a bug:

InputForm[CylinderIntegrandd\[Theta]d\[Zeta]]
  is
(R*(R - \[Rho]*Cos[\[Alpha] - \[Theta]]))/(3*(R^2 + (z - \[Zeta])^2 +
\[Rho]^2 - 2*R*\[Rho]*Cos[\[Alpha] - \[Theta]])^3)

InputForm[assumptions] is
{R > 0, L > 0, \[Rho] > 0, Element[\[Zeta], Reals], Element[z, Reals],
\[Alpha] >= 0, \[Alpha] <= 2*Pi}

Integrate[CylinderIntegrandd\[Theta]d\[Zeta], {\[Theta], 0, 2 \[Pi]},
  Assumptions -> assumptions]

returns 0.

I think that this is not correct.

Craig


PS: I know that the L>0 is superfluous in the assumptions, but I use
assumptions over again.



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

> Date: Thu, 4 Oct 2007 10:42:55 -0400 (EDT)
> From: W. Craig Carter <ccarter at mit.edu>
> To: mathgroup at smc.vnet.net
> Subject: (Never Mind? Can't duplicate result!) Re: [mg81827] Can
>     Integrate[expr,{x,a,b}] give an incorrect result?
> 
>
> 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]
>> 
>>
>>  Something isn't adding up??
>>
>>  Thanks, WCC
>> 
>> 
>
>

• References:
  • Can Integrate[expr,{x,a,b}] give an incorrect result?
    • From: "W. Craig Carter" <ccarter@mit.edu>