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MathGroup Archive 2002

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Re: Re: Integrating over a Minimum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32986] Re: [mg32980] Re: [mg32946] Integrating over a Minimum
  • From: BobHanlon at aol.com
  • Date: Sat, 23 Feb 2002 02:38:03 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2/22/02 3:30:56 AM, tgarza01 at prodigy.net.mx writes:

>I take the example you give. Try NIntegrate instead of Integrate:
>
>In[1]:=
>NIntegrate[Min[x, y], {y, 0, 1}, {x, 0, 1}]
>Out[1]=
>0.33333
>
>I quote from the Help Browser: "Integrate can evaluate integrals of rational
>functions. It can also evaluate integrals that involve exponential,
>logarithmic, trigonometric and inverse trigonometric functions, so long
>as
>the result comes out in terms of the same set of functions." If you're
>interested in numerical results - which I assume is the case - I think
>you
>can successfully use NIntegrate. Another example:
>
>In[1]:=
>f[x_, y_] := x + y /; 0 <= x <= 1 && 0 <= y <= 1;
>f[x_, y_] := x + 2*y /; x >= 1 || y >= 1;
>
>In[2]:=
>NIntegrate[f[x, y], {x, 0, 2}, {y, 0, 2}]
>Out[2]=
>11.5
>

Alternatively, break the integral into segments: 
0<=x<=y and y<=x<=1

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

1/3


Bob Hanlon
Chantilly, VA  USA


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