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 [