Re: Re: Integration

• To: mathgroup at smc.vnet.net
• Subject: [mg44060] Re: [mg43955] Re: Integration
• From: "Peter Pein" <nospam at spam.no>
• Date: Sun, 19 Oct 2003 02:00:20 -0400 (EDT)
• References: <bmg0li\$e9k\$1@smc.vnet.net> <200310150859.EAA26393@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Curt,

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

Your definition for f defines it as a function of one or more variables,
not as a simple expression.

In[1]:=
(* you thought, Alex did : *)
f = x;
Integrate[f[x], {x, x0, x1}]
Remove[f];
Out[2]=
Integrate[x[x], {x, x0, x1}]
In[4]:=
(* you thought you did : *)
f[x_] := x;
Integrate[f[x], {x, x0, x1}]
Remove[f];
Out[5]=
2     2
-x0    x1
---- + ---
2      2
In[7]:=
(* but you did: *)
f[x_] := x;
Integrate[f, {x, x0, x1}]
Out[8]=
-(f x0 ) + f x1

Peter Pein, Berlin
petsie at arcAND.de
replace && by || to write to me

----- Original Message -----
From: "Curt Fischer" <crf3 at po.cwru.edu>
To: mathgroup at smc.vnet.net
Subject: [mg44060] [mg43955] Re: Integration

> 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.
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> > 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
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> >
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> > *******************************************************************)
> >
> > (*CacheID: 232*)
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> >
> > (*NotebookFileLineBreakTest
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> > (*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
> >
>
>

```

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