Re: Error in integrals?
- To: mathgroup at smc.vnet.net
- Subject: [mg9500] Re: Error in integrals?
- From: Josip Loncaric <josip at icase.edu>
- Date: Sat, 8 Nov 1997 23:04:31 -0500
- Organization: ICASE
- Sender: owner-wri-mathgroup at wolfram.com
The integral in question has a branch cut at m=0.267949 -- to see that,
just plot the result of Integrate[ior[m],m] from m=0 to m=1. Adjust
for this jump of 2.1547, and you get the correct answer (also produced
by NIntegrate).
Josip
steve at smc.vnet.net wrote:
>
> Mathematica 3.0 on a PowerMac 7200/90 88MB Mac OS 8 gives different
> results for Integrate vs. NIntegrate.
>
> Here is one example.
>
> ior[m_] := 1/3*(2*Sqrt[3]*Sqrt[(-1 + m^2)^2/(1 + m^2)^4] +
> Sqrt[(Sqrt[3] - 6*m - Sqrt[3]*m^2)^2/(1 + m^2)^4] + Sqrt[(Sqrt[3] +
> 6*m - Sqrt[3]*m^2)^2/(1 + m^2)^4])
>
> In[31]:=
> N[Integrate[ior[m],{m,0,1}]]
>
> Out[31]=
> -0.42265
>
> In[32]:=
> NIntegrate[ior[m],{m,0,1}]
>
> Out[32]=
> 1.73206
>
> What am I doing wrong ? Which answer is correct ?
>
> Cliff Nelson
--
Dr. Josip Loncaric, Senior Staff Scientist ICASE, M/S 403, NASA Langley
Research Center, Hampton, VA 23681-0001 Phone: (757) 864-2192
mailto:josip at icase.edu Fax: (757) 864-6134
http://www.icase.edu/~josip/