       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:=
Integrate[Sqrt[1+(y'[t]/x'[t])^2]*x'[t],{t,0,2Pi}]

Out=
2
y'[t]
Integrate[x'[t] Sqrt[1 + ------], {t, 0, 2 Pi}]
2
x'[t]

In:=
\$Version

Out=
5.2 for Microsoft Windows (June 20, 2005)

(* And in version 6.0.1 *)

In:= Integrate[Sqrt[1 + (y'[t]/x'[t])^2]*x'[t], {t, 0, 2 Pi}]

Out=
2
y'[t]
Integrate[x'[t] Sqrt[1 + ------], {t, 0, 2 Pi}]
2
x'[t]

In:= \$Version

Out= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"

Regards,
--
Jean-Marc

```

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