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>*Reply-to*: drmajorbob at yahoo.com

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

**References**:**Calculus and InterpolatingFunction***From:*Just A Stranger <forpeopleidontknow@gmail.com>