Re: Integration error in 5.0?

• To: mathgroup at smc.vnet.net
• Subject: [mg48839] Re: Integration error in 5.0?
• From: "Peter Pein" <petsie at arcor.de>
• Date: Fri, 18 Jun 2004 02:13:10 -0400 (EDT)
• References: <cabql1\$ouc\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Richard Ollerton" <r.ollerton at uws.edu.au> schrieb im Newsbeitrag
news:cabql1\$ouc\$1 at smc.vnet.net...
> I used Mathematica 5.0 (Windows 2000) to find the value of an integral
> representing the volume under the sphere x^2 + y^2 + z^2 = 4 and above the
> cone z = 2 Sqrt(x^2 + y^2) (just to check my own calculation).  The value
> given for the analytical calculation in Cartesian coordinates using
> Integrate is incorrect while exactly the same integral using NIntegrate is
> correct as confirmed by the equivalent version in spherical coordinates.
>
>
4Integrate[1,{x,0,2/Sqrt[5]},{y,0,Sqrt[4/5-x^2]},{z,2Sqrt[x^2+y^2],Sqrt[4-x^
> 2-y^2]}]
>
> gives -32Pi/(3Sqrt[5])
>
> while
>
>
4NIntegrate[1,{x,0,2/Sqrt[5]},{y,0,Sqrt[4/5-x^2]},{z,2Sqrt[x^2+y^2],Sqrt[4-x
> ^2-y^2]}]
>
> gives 1.76889
>
...
> Has this been noticed previously?
>
>
> Richard Ollerton
>

must be one of the numerous features of version 5

In[1]:= \$Version
4*Integrate[1, {x, 0, Sqrt[4/5]}, {y, 0, Sqrt[4/5 - x^2]},
{z, 2*Sqrt[x^2 + y^2], Sqrt[4 - x^2 - y^2]}]
N[%]
Out[1]= "4.0 for Microsoft Windows (July 16, 1999)"
Out[2]= 16/15*(5 - 2*Sqrt[5])*Pi
Out[3]= 1.7688893929253466

--
Peter Pein, Berlin
to write to me, start the subject with [

```

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