       Re: Calculus and InterpolatingFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg121622] Re: Calculus and InterpolatingFunction
• From: Richard Hofler <rhofler at bus.ucf.edu>
• Date: Thu, 22 Sep 2011 07:27:33 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109210933.FAA13140@smc.vnet.net>

```Hello,

One straightforward solution is to transform the values in the list that you call data.

(* display the list for comparison later *)
data=RandomReal[#]*2&/@Range[1,10]

(* display the new list to confirm that it is correctly transformed  *)
newdata=Flatten[(1+#)&/@data]
g=Interpolation[newdata];
Integrate[g[x],{x,1,10}]

{0.293708,2.9835,1.05602,5.14945,2.92964,6.02907,13.5116,5.89785,8.41953,11.2031}

{1.29371,3.9835,2.05602,6.14945,3.92964,7.02907,14.5116,6.89785,9.41953,12.2031}
61.7534

Richard

-----Original Message-----
From: Just A Stranger [mailto:forpeopleidontknow at gmail.com]
Sent: Wednesday, September 21, 2011 5:33 AM
To: mathgroup at smc.vnet.net
Subject: [mg121622] Calculus and InterpolatingFunction

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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