Re: Possible mis-documentation

• To: mathgroup at smc.vnet.net
• Subject: [mg20479] Re: Possible mis-documentation
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Wed, 27 Oct 1999 02:04:46 -0400
• References: <7v3e6h\$651@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Philip C Mendelsohn (Philip C Mendelsohn) <mend0070 at tc.umn.edu> wrote in
message news:7v3e6h\$651 at smc.vnet.net...
> I happened to notice a line in the documentation for Integrate.
> The book says that "Multiple Integrals use a variation of
> standard iterator notation.  The first variable given
> corresponds to the outermost integral and is done last."
>
> Can I get some confirmation?  I am running v4.0.1 under Linux, and
> *SEEM* to have determined that the manual is incorrect and
> that it does in fact do the innermost variable with the
> innermost integral.  However, I got my head turned around
> pretty well, so may have not got this correct.
>
> In indefinite integrals, it doesn't matter most times, but for
> definite multiple integrals, either the manual is wrong, or I
> am making exactly the same mistake as M!
>
> Thanks very much,
>
> Phil Mendelsohn
>
> --
> if (\$income > \$expenses OR \$time != \$money )
> set hell_frozen=true;
> asif
>

Phil,

There is a difference depending on whether you are using Input form.

The following shows that the order is as stated in the book - the order of
integration is by y then by x  - outside in

Integrate[ x^2 + y^2, {x,0,1}, {y,0,x}]

1/3

-  compare the  previous result with the following two

Integrate[Integrate[ x^2 + y^2,  {y,0,x}],{x,0,1}]

1/3

Integrate[Integrate[x^2 + y^2, {x, 0, 1}], {y, 0, x}]

x/3 + x^3/3

However in Standard and Traditional forms the integral signs (with limits)
and the differential signs are separated and the integration is inside out:

\!\(\[Integral]\_0\%1\(\[Integral]\_0\%x\((x\^2 +
y\^2)\) \[DifferentialD]y \[DifferentialD]x\)\)

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

```

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