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. 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}] 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