MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Possible mis-documentation

  • To: mathgroup at
  • Subject: [mg20479] Re: Possible mis-documentation
  • From: "Allan Hayes" <hay at>
  • Date: Wed, 27 Oct 1999 02:04:46 -0400
  • References: <7v3e6h$>
  • Sender: owner-wri-mathgroup at

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


There is a difference depending on whether you are using Input form.
StandardForm or Traditional 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}]


-  compare the  previous result with the following two

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


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 Hayes
Mathematica Training and Consulting
Leicester UK
hay at
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

  • Prev by Date: Re: Basic Laplace Transforms
  • Next by Date: Re: Non standard evaluation troubles.
  • Previous by thread: Possible mis-documentation
  • Next by thread: graphics