Re: Bug of Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg83023] Re: Bug of Integrate
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 8 Nov 2007 06:03:22 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <fg4dfv$6c3$1@smc.vnet.net><fg6pse$d44$1@smc.vnet.net> <fgs908$4m9$1@smc.vnet.net>
Miguel wrote:
<snip>
> By other hand, I think everybody knows the solution of the following
> problem:
> "Derive the formula for the circunference of a circle of radius "a" by
> computing the length of the arc x=a cost; y= a sint for 0<=t<=Pi
> "
>
> L=Integrate[Sqrt[1+(y'[t]/x'[t])^2]*x'[t],{t,0,2Pi}]
>
> I have tried to resolve with version 5.2 and version 6.0.1. The
> results have been differents.
<snip>
It would have been interesting to post both results. On my system, the
posted integral returned unevaluated on both systems.
In[1]:=
Integrate[Sqrt[1+(y'[t]/x'[t])^2]*x'[t],{t,0,2Pi}]
Out[1]=
2
y'[t]
Integrate[x'[t] Sqrt[1 + ------], {t, 0, 2 Pi}]
2
x'[t]
In[2]:=
$Version
Out[2]=
5.2 for Microsoft Windows (June 20, 2005)
(* And in version 6.0.1 *)
In[1]:= Integrate[Sqrt[1 + (y'[t]/x'[t])^2]*x'[t], {t, 0, 2 Pi}]
Out[1]=
2
y'[t]
Integrate[x'[t] Sqrt[1 + ------], {t, 0, 2 Pi}]
2
x'[t]
In[2]:= $Version
Out[2]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"
Regards,
--
Jean-Marc