Re: When does Integrate give incorrect results?
- To: mathgroup at smc.vnet.net
- Subject: [mg37525] Re: [mg37460] When does Integrate give incorrect results?
- From: Vladimir Bondarenko <vvb at mail.strace.net>
- Date: Sat, 2 Nov 2002 03:32:06 -0500 (EST)
- References: <200210310941.EAA18281@smc.vnet.net>
- Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
- Sender: owner-wri-mathgroup at wolfram.com
strgh at mimosa.csv.warwick.ac.uk writes on Thursday, October 31, 2002, 5:41:23 AM :
strgh> Is there any guide as to when Mathematica gives incorrect
strgh> results for an integral? For example,
strgh> Integrate[ 1/(1 + x^2y^2), {x, 0, Infinity}, {y, 0, x} ]
strgh> returns 0.
It is safer to use the following syntax
In[1] := $Version
Out[1] = 4.2 for Microsoft Windows (June 5, 2002)
In[2] := Integrate[Integrate[1/(1 + x^2y^2), {x, 0, Infinity}], {y, 0, x}]
Out[2] = Integrate::idiv : Integral of (Log[-I y] - Log[-I y])/y does not converge on {0, x}.
Integrate::idiv : Integral of (Log[-I y] - Log[-I y])/y does not converge on {0, x}.
(I/2)*Integrate[(Log[(-I)*y] - Log[I*y])/y, {y, 0, x}]
As you can see, Mathematica returns the correct output.
The same holds for the following versions
4.1 for Microsoft Windows (November 2, 2000)
4.0 for Microsoft Windows (April 21, 1999)
The version for Microsoft Windows 3.0 (April 25, 1997) yields
Integrate[If[Arg[y^2] != Pi, Pi/(2*Sqrt[y^2]),
Integrate[(1 + x^2*y^2)^(-1), {x, 0, Infinity}]], {y, 0, x}]
The version for Windows 387 2.2 (April 9, 1993) returns
(Pi*Integrate[(y^2)^(-1/2), {y, 0, x}])/2
The version for Windows (September 27, 1989) returns...
In case if you still use the version 1.2 for Microsoft Windows
(September 27, 1989)... well... why do NOT consider the
golden opportunity of the upgrade? ;-)
Best wishes,
Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group
Email: vvb at mail.strace.net
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