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Re: Calculus and InterpolatingFunction


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

(* display the list for comparison later *)

(* display the new list to confirm that it is correctly transformed  *)




-----Original Message-----
From: Just A Stranger [mailto:forpeopleidontknow at]
Sent: Wednesday, September 21, 2011 5:33 AM
To: mathgroup at
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.

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

>  Integrate[f[x], {x, 1, 10}]

So far so good. But just a little bit of arithmetic in the integral and it doesn't work anymore:
Integrate[f[x]+1, {x, 1, 10}]
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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