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Topic: Integrating an InterpolatingFunction times another function
Replies: 2   Last Post: Apr 14, 2012 3:16 AM

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 Yi Wang Posts: 21 Registered: 3/30/12
Re: Integrating an InterpolatingFunction times another function
Posted: Apr 14, 2012 3:09 AM

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

Date Subject Author
4/13/12 Andrew DeYoung
4/14/12 Yi Wang
4/14/12 Albert Retey