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?
>
> (************** Content-type: application/mathematica **************
>                      CreatedBy='Mathematica 4.2'
>
>                     Mathematica-Compatible Notebook
>
> This notebook can be used with any Mathematica-compatible
> application, such as Mathematica, MathReader or Publicon. The data
> for the notebook starts with the line containing stars above.
>
> To get the notebook into a Mathematica-compatible application, do
> one of the following:
>
> * Save the data starting with the line of stars above into a file
>   with a name ending in .nb, then open the file inside the
>   application;
>
> * Copy the data starting with the line of stars above to the
>   clipboard, then use the Paste menu command inside the application.
>
> Data for notebooks contains only printable 7-bit ASCII and can be
> sent directly in email or through ftp in text mode.  Newlines can be
> CR, LF or CRLF (Unix, Macintosh or MS-DOS style).
>
> NOTE: If you modify the data for this notebook not in a Mathematica-
> compatible application, you must delete the line below containing
> the word CacheID, otherwise Mathematica-compatible applications may
> try to use invalid cache data.
>
> applications, contact Wolfram Research:
>   web: http://www.wolfram.com
>   email: info at wolfram.com
>   phone: +1-217-398-0700 (U.S.)
>
> Notebook reader applications are available free of charge from
> Wolfram Research.
> *******************************************************************)
>
> (*CacheID: 232*)
>
>
> (*NotebookFileLineBreakTest
> NotebookFileLineBreakTest*)
> (*NotebookOptionsPosition[      2944,         84]*)
> (*NotebookOutlinePosition[      3586,        106]*)
> (*  CellTagsIndexPosition[      3542,        102]*)
> (*WindowFrame->Normal*)
>
>
>
> 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)\);\)\(\
> \[IndentingNewLine]\)
>     \)\), "\[IndentingNewLine]",
>     \(Integrate[f, {\[Lambda], \[Xi], \[Infinity]}]\)}], "Input"],
>
> Cell[BoxData[
>     \(Sum::"div" \(\(:\)\(\ \)\) "Sum does not converge."\)],
> "Message"],
>
> Cell[BoxData[
>     \(Sum::"div" \(\(:\)\(\ \)\) "Sum does not converge."\)],
> "Message"],
>
> Cell[BoxData[
>     \(Sum::"div" \(\(:\)\(\ \)\) "Sum does not converge."\)],
> "Message"],
>
> Cell[BoxData[
>     \(General::"stop" \(\(:\)\(\ \)\)
>       "Further output of \!\(Sum :: \"div\"\) will be suppressed
> during this \
> calculation."\)], "Message"],
>
> Cell[BoxData[
>     \(\$Aborted\)], "Output"]
> }, Open  ]]
> },
> FrontEndVersion->"4.2 for Microsoft Windows",
> ScreenRectangle->{{0, 720}, {0, 407}},
> WindowSize->{683, 346},
> WindowMargins->{{0, Automatic}, {Automatic, 0}}
> ]
>
> (*******************************************************************
> 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->{}
> *)
>
> (*CellTagsIndex
> CellTagsIndex->{}
> *)
>
> (*NotebookFileOutline
> Notebook[{
>
> Cell[CellGroupData[{
> Cell[1776, 53, 677, 11, 199, "Input"],
> Cell[2456, 66, 86, 1, 24, "Message"],
> Cell[2545, 69, 86, 1, 24, "Message"],
> Cell[2634, 72, 86, 1, 24, "Message"],
> Cell[2723, 75, 160, 3, 42, "Message"],
> Cell[2886, 80, 42, 1, 29, "Output"]
> }, Open  ]]
> }
> ]
> *)
>
>
>
> (*******************************************************************
> End of Mathematica Notebook file.
> *******************************************************************)
>
> Alex
>

```

• Prev by Date: Re: What Happens to Garbage in Mathematica?
• Next by Date: Concentric contours about the centroid, having the same length, and interior to an initial contour.