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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