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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


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