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MathGroup Archive 2003

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Re: Integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43955] Re: Integration
  • From: "Curt Fischer" <crf3 at po.cwru.edu>
  • Date: Wed, 15 Oct 2003 04:59:32 -0400 (EDT)
  • References: <bmg0li$e9k$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Alex,

Spend some minutes going through the introductory help material in the Help
Browser.

Your definition for f defines it as a simple expression, not as a function
of one or more variables.  But even after fixing this mistake, I couldn't
get Mathematica to return a value for the indefinite integral.  Changing the
infinity to an arbitrary constant changed the result, though:

In[12]:=
Clear[f];


In[13]:=
\!\(\(f[\[Lambda]_] := \(\(\(2\) \(\[Pi]\)\(\ \)\(b\)\(\ \)\)\/a\) \((3 \(
e\^2\) \((x\/\[Lambda]\^2 + \(\[ImaginaryI]\ y\)\/\(\
\[Lambda]\^2 - e\^2\))\)
1\/\(\[Lambda] \((\[Lambda]\^2 - e\^2)\) \(\@\(\(a\^2\) \
\[Lambda]\^2 - l1\^2\)\) \@\(\(a\^2\) \[Lambda]\^2 - l2\^2\)\) - \(\((x\/\
\[Lambda]\^2 + \(\[ImaginaryI]\ y\)\/\(\[Lambda]\^2 - e\^2\))\)\^3\)
\(\(a\^2\
\) \(\[Lambda]\^3\) \((\[Lambda]\^2 - e\^2)\)\)\/\((\(\@\(\(a\^2\) \
\[Lambda]\^2 - l1\^2\)\) \@\(\(a\^2\) \[Lambda]\^2 - l2\^2\))\)\^3)\);\)\)


In[14]:=


Integrate[f, {\[Lambda], \[Xi], \[CapitalXi]}]


Out[14]=
f (-\[Xi] + \[CapitalXi])

Does that help any?

-- 
Curt Fischer


"Alex" <akhmel at hotmail.com> wrote in message
news:bmg0li$e9k$1 at smc.vnet.net...
> I tried to compute some elementary integrals (see below). Mathematica
> spent a couple of hours and didn't give any result. Any advice?
>
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>
>
>
> Notebook[{
>
> Cell[CellGroupData[{
> Cell[BoxData[{
>     \(\(\(f = \(\(\(2\)  \(\[Pi]\)\(\ \)\(b\)\(\ \)\)\/a\) \((3 \(
>                     e\^2\) \((x\/\[Lambda]\^2 + \(\[ImaginaryI]\
> y\)\/\(\
> \[Lambda]\^2 - e\^2\))\)
>                 1\/\(\[Lambda] \((\[Lambda]\^2 - e\^2)\)
> \(\@\(\(a\^2\) \
> \[Lambda]\^2 - l1\^2\)\) \@\(\(a\^2\) \[Lambda]\^2 - l2\^2\)\) -
> \(\((x\/\
> \[Lambda]\^2 + \(\[ImaginaryI]\ y\)\/\(\[Lambda]\^2 - e\^2\))\)\^3\)
> \(\(a\^2\
> \) \(\[Lambda]\^3\) \((\[Lambda]\^2 - e\^2)\)\)\/\((\(\@\(\(a\^2\) \
> \[Lambda]\^2 - l1\^2\)\) \@\(\(a\^2\) \[Lambda]\^2 -
> l2\^2\))\)\^3)\);\)\(\
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> "Message"],
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> during this \
> calculation."\)], "Message"],
>
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>     \($Aborted\)], "Output"]
> }, Open  ]]
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> WindowMargins->{{0, Automatic}, {Automatic, 0}}
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>
> (*******************************************************************
> Cached data follows.  If you edit this Notebook file directly, not
> using Mathematica, you must remove the line containing CacheID at
> the top of  the file.  The cache data will then be recreated when
> you save this file from within Mathematica.
> *******************************************************************)
>
> (*CellTagsOutline
> CellTagsIndex->{}
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>
> Alex
>



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