Re: Calculus and InterpolatingFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg121603] Re: Calculus and InterpolatingFunction
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 22 Sep 2011 07:24:08 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109210933.FAA13140@smc.vnet.net>

```NIntegrate works, and it's a more natural choice when symbolic methods are
clearly unworkable:

data = RandomReal[#]*2 & /@ Range[1, 10];
f = Interpolation[data];
NIntegrate[f[x], {x, 1, 10}]

37.5601

NIntegrate[f[x] + 1, {x, 1, 10}]

46.5601

Bobby

On Wed, 21 Sep 2011 04:33:18 -0500, 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[1]:=
> data = RandomReal[#]*2 & /@ Range[1, 10];
> f = Interpolation[data];
>
>>  Integrate[f[x], {x, 1, 10}]
> Out[1]:=40.098
>
> So far so good. But just a little bit of arithmetic in the integral and
> it
> doesn't work anymore:
> In[2]:=
> Integrate[f[x]+1, {x, 1, 10}]
> Out[2]:=
> 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 ?

--
DrMajorBob at yahoo.com

```

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