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Re: Integrating an InterpolatingFunction times another function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126070] Re: Integrating an InterpolatingFunction times another function
  • From: A Retey <awnl at gmx-topmail.de>
  • Date: Sat, 14 Apr 2012 03:13:15 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jm8q6r$j74$1@smc.vnet.net>

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?

Use NIntegrate. It's probably worth noting that it is a very special 
feature that integration of just interpolating functions works 
symbolically, you can even get another interpolating function for the 
indefinite integral, e.g.:

Integrate[ifun[x],x]


hth,

albert



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