Re: Calculus and InterpolatingFunction

*To*: mathgroup at smc.vnet.net*Subject*: [mg121608] Re: Calculus and InterpolatingFunction*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Thu, 22 Sep 2011 07:25:02 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Reply-to*: hanlonr at cox.net

data = RandomReal[#]*2 & /@ Range[1, 10]; f = Interpolation[data]; Integrate[f[x], {x, 1, 10}] 52.9041 Use NIntegrate NIntegrate[f[x] + 1, {x, 1, 10}] 61.9041 Or Map over the expression Integrate[#, {x, 1, 10}] & /@ (f[x] + 1) 61.9041 Bob Hanlon ---- 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 ?

**Follow-Ups**:**Re: Calculus and InterpolatingFunction***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: Calculus and InterpolatingFunction***From:*Brentt <brenttnewman@gmail.com>

**Re: Calculus and InterpolatingFunction***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: Calculus and InterpolatingFunction***From:*Murray Eisenberg <murray@math.umass.edu>