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MathGroup Archive 2004

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Re: NIntegrate a list

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52978] Re: NIntegrate a list
  • From: Simon Anders <simon.anders at uibk.ac.at>
  • Date: Sat, 18 Dec 2004 04:00:08 -0500 (EST)
  • Organization: University of Innsbruck, Austria
  • References: <cpug13$gna$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Aaron,

Aaron Fude wrote:

> I can Integrate this, but apparently not NIntegrate this:
> 
> Integrate[x*Sin[x]*{1, 2}, {theta, -Pi, Pi}]
> 
> but not
> 
> NIntegrate[x*Sin[x]*{1, 2}, {theta, -Pi, Pi}]
> 
> Is there a good way to do this (w/o writing loops)?

First, I assume, you meant x instead of theta:

   NIntegrate[x*Sin[x]*{1, 2}, {x, -Pi, Pi}]

Now, you can, of course, put N[_] around it:

   N[Integrate[x*Sin[x]*{1, 2}, {x, -Pi, Pi}]]

But this might try to do it first analytically, which you do not want. 
So, use Map:

   Map [NIntegrate[x*Sin[x]*#, {x, -Pi, Pi}] &, {1, 2}]

(In case, you are not too experienced, let me explain: I have written 
the left argument to 'Map' as "pure function", i.e. a function where the 
parameters are referred to not by name but by position, i.e. we write 
'#1', '#2', '#3' etc. for them, or here, just '#', which is short for 
'#1', the one and only parameter of the function. The '&' at the end 
marks the construct before it as pure fucntion. And 'Map' takes the 
elements of the second parameter, the list, and puts them into the 
position maked with the '#'. This is, by the way, precisely, what 
Mathemtica does automatically in the first case (Integrate without N).)

HTH,
   Simon


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