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MathGroup Archive 1997

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Re: NIntegrate where terms of integrand have unknown constant coefficients

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8954] Re: [mg8882] NIntegrate where terms of integrand have unknown constant coefficients
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 6 Oct 1997 01:59:22 -0400
  • Organization: University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

David Withoff wrote:

> I would do this by defining your own function that performs the
> symbolic linearity operations before calling NIntegrate, rather
> than by redefining NIntegrate.  For example
> 
> In[1]:= int[p_Plus, q_] := Map[int[#, q] &, p]
> 
> In[2]:= int[(p:c[_]) f_, q_] := p NIntegrate[f, q]
> 
> In[3]:= int[c[1] x + c[2] x^2, {x, 0, 1}]
> 
> Out[3]= 0.5 c[1] + 0.333333 c[2]
> 
> This strategy could be made considerably more elaborate to do
> almost anything that you might want.

Another general and powerful way, is to use pattern-matching:

  In[1]:= f[n_][x_] = x^n;

  In[2]:= c[1] f[1][x] + c[2] f[2][x] /. c[n_] a_ :> c[n] NIntegrate[a,
{x, 0, 1}]
  
  Out[2]= 0.5 c[1] + 0.333333 c[2]

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia           
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au 
AUSTRALIA                             http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
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