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
____________________________________________________________________

```

• Prev by Date: Setting precision in binary digits?
• Next by Date: Re: NIntegrate where terms of integrand have unknown constant coefficients
• Previous by thread: Re: NIntegrate where terms of integrand have unknown constant coefficients
• Next by thread: Re: NIntegrate where terms of integrand have unknown constant coefficients