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Re: How to specify these limits in an integral?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63455] Re: How to specify these limits in an integral?
  • From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 1 Jan 2006 01:16:08 -0500 (EST)
  • Organization: The Open University, Milton Keynes, U.K.
  • References: <dp5rch$rjs$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Konrad Den Ende" <chamster at home.se> a écrit dans le message de news: 
dp5rch$rjs$1 at smc.vnet.net...
|
| I have a double integral of the function f = x * y. I'd
| like make Mathematica compute it's value over the
| disc specified by, let's say:
| x^2 + y^2 - 2x + 6y <=6
|
| I can carry out computation on paper, preparing the
| sutabile substitutions myself but i wonder if there's
| a way to shove it all into Mathematica and let it chew.
|
| Sincerely
| Konrad
|
|

Hi Konrad,

Have a look at the *Boole* function 
(http://documents.wolfram.com/mathematica/functions/Boole) and at the 
_Mathematica_Book_, section "3.5.9 Integrals over Regions" 
(http://documents.wolfram.com/mathematica/book/section-3.5.9). In your case 
you could write your integral as

In[1]:=
f[x_, y_] := x*y

In[2]:=
Integrate[f[x, y]*Boole[x^2 + y^2 - 2*x + 6*y <= 6],
  {x, -10, 10}, {y, -10, 10}]

Out[2]=
-48*Pi

Best regards,
/J.M. 



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