Re: Calculus and InterpolatingFunction

*To*: mathgroup at smc.vnet.net*Subject*: [mg121625] Re: Calculus and InterpolatingFunction*From*: "Kevin J. McCann" <Kevin.McCann at umbc.edu>*Date*: Thu, 22 Sep 2011 07:28:06 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j5cb71$cvl$1@smc.vnet.net>

You need to use NIntegrate. Kevin On 9/21/2011 5:36 AM, Just A Stranger 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 ?