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Re: Numerical integration and list of points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87654] Re: [mg87622] Numerical integration and list of points
  • From: Curtis Osterhoudt <cfo at lanl.gov>
  • Date: Tue, 15 Apr 2008 05:49:52 -0400 (EDT)
  • Organization: LANL
  • References: <200804141053.GAA13528@smc.vnet.net>
  • Reply-to: cfo at lanl.gov

  Hi, Gueromo, 

       It seems to work for me:

In[1]:= data = ({#1, Sin[13.4*#1]} & ) /@ Range[0, 4, 0.01]; 
f = Interpolation[data];
NIntegrate[f[x], {x, 0, 4}]
Integrate[f[x], {x, 0, 4}]
Integrate[Sin[a*x], x]
% /. a -> 13.4
(% /. {x -> 4}) - (% /. {x -> 0})


During evaluation of In[1]:= NIntegrate::ncvb: NIntegrate failed to \
converge to prescribed accuracy after 9 recursive bisections in x \
near {x} = {0.126211}. NIntegrate obtained 0.14786850709355207` and \
1.9590212682839143`*^-7 for the integral and error estimates. >>

Out[3]= 0.147869

Out[4]= 0.147869

Out[5]= -(Cos[a x]/a)

Out[6]= -0.0746269 Cos[13.4 x]

Out[7]= 0.147869



On Monday 14 April 2008 04:53:33 guerom00 wrote:
> Hello everyone,
>
> I have a function which I read as a list of points. I want then to
> estimate its integral. I do more or less this :
>
> data={{x1,y1},{x2,y2},...,{xN,yN}}
> f=Interpolation[data]
> NIntegrate[f[x],{x,x1,xN}]
>
> Is it the correct way ? Because Mathematica hangs without giving me an
> answer although it seems a pretty straightforward thing to do...
>
> Thanks for any suggestions.



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