       Re: Calculus and InterpolatingFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg121614] Re: Calculus and InterpolatingFunction
• From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
• Date: Thu, 22 Sep 2011 07:26:07 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109210933.FAA13140@smc.vnet.net>

```Hi Stranger

Unless you're wedded to Integrate[...], NIntegrate[...] works in this case:

data = RandomReal[#]*2 & /@ Range[1, 10]
f = Interpolation[data]
Plot[f[x], {x, 1, 10}]
int1 = Integrate[f[x], {x, 1, 10}]
ClearAll[ ff ]
ff[x_] := f[x] + 1
{f, ff}
Plot[ff[x], {x, 1, 10}]
int2 = NIntegrate[ff[x], {x, 1, 10}]
int2 - int1

Cheers

Barrie

>>> On 21/09/2011 at 7:33 pm, in message <201109210933.FAA13140 at smc.vnet.net>, Just
A Stranger <forpeopleidontknow at gmail.com> wrote:
> I'm trying to get a definite integral for an InterpolatingFunction. It works
> if it is the function by itself, but not for some reason arithmetically
> combining the InterpolatingFunction with another function makes it not
> return a value. e.g.
>
>
> In:=
> data = RandomReal[#]*2 & /@ Range[1, 10];
> f = Interpolation[data];
>
>>  Integrate[f[x], {x, 1, 10}]
> Out:=40.098
>
> So far so good. But just a little bit of arithmetic in the integral and it
> doesn't work anymore:
> In:=
> Integrate[f[x]+1, {x, 1, 10}]
> Out:=
> Integrate[Plus[1, InterpolatingFunction[][x]], List[x, 1, 10]]
>
> (That last answer was actually the output with  //FullForm applied)
> Why won't it give me a numerical evaluation? Is there anyway to make a
> continuous function from data that will seemlessly work with Integrate? I'm
> thinking of constructing a piecwise function using Fit, Piecwise, and a
> Table for the arguments to Piecewise. But I would think  Interpolation might
> have worked and been easier. I want to figure out if I am I doing something
> wrong with Interpolation before I start trying to tackle a slightly more
> complicated piecewise defined function ?

```

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