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Re: Integrating an InterpolatingFunction times another function

• To: mathgroup at smc.vnet.net
• Subject: [mg126073] Re: Integrating an InterpolatingFunction times another function
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 14 Apr 2012 03:14:17 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201204130857.EAA19506@smc.vnet.net>

Use NIntegrate

points = {{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}};

Clear[ifun, g]

ifun = Interpolation[points];

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

32.3167


Bob Hanlon


On Fri, Apr 13, 2012 at 4:57 AM, Andrew DeYoung <adeyoung at andrew.cmu.edu> 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
>

• References:
  • Integrating an InterpolatingFunction times another function
    • From: Andrew DeYoung <adeyoung@andrew.cmu.edu>