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Re: Integrating an InterpolatingFunction times another function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126057] Re: Integrating an InterpolatingFunction times another function
  • From: Yi Wang <tririverwangyi at gmail.com>
  • Date: Sat, 14 Apr 2012 03:08:45 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jm8q6r$j74$1@smc.vnet.net>

Hi, Andrew,

I guess Interpolation is more useful numerically. If you want a result, try

NIntegrate[x*ifun[x], {x, 1, 5}]

On the other hand, if you want an exact result:

ifun2 = InterpolatingPolynomial[points, x]

Integrate[x*ifun2, {x, 1, 5}]

On Friday, April 13, 2012 5:04:27 AM UTC-4, Andrew DeYoung wrote:
> Hi,
> 
> I have made a sample InterpolatingFunction:
> 
> points = {{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}};
> ifun = Interpolation[points]
> 
> The following integral computes fine:
> 
> Integrate[ifun[x], {x, 1, 5}]
> 
> However, this integral will not be evaluated:
> 
> Integrate[x*ifun[x], {x, 1, 5}]
> 
> Why will this integral not be computed?  Is there any way that I can
> compute this integral?
> 
> Thank you kindly!
> 
> Andrew DeYoung
> Carnegie Mellon University




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