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MathGroup Archive 2001

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Re: NIntegrate and Plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30461] Re: NIntegrate and Plot
  • From: Yasvir Avindra Tesiram <y.tesiram at pgrad.unimelb.edu.au>
  • Date: Wed, 22 Aug 2001 01:41:58 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Thank for all the replies. Once again I am overwhelmed by the number of
ways in which one problem can be tackled with Mathematica. Nothing like
learning by example. However, I have one more request and if possible,
using the method as outlined by Tom Burton below, whether FF below could
be used once again to perform a similar integration, i.e., I now want to
integrate the integral again and plot the result. I assume that
ListIntegrate and InterpolationFunction could be used somehow on FF after
Partitioning FF.

Below is a re-typed copy of the notebook with Tom Burtons construct for
making a ListPlot of the first integral. 

Any tips on making this a small package so that the function can be
changed (e.g. func_ -> Sech, Sin, Cos) would also be much appreciated. I
have seen Roman Maeders example on the Parametric Plots and will probably
follow that by example.

Thanks
Yas


fco=0.01;
np=100;
beta1 = -4.6341 * Log[10,fco] + 1.3031;
betaN = 2^(n-1) * beta1;
 
f[x_] := (Sech[betaN * x^n])^2
 
 (*First, define a function to integrate over an interval:*)

DF[{x1_, x2_}] := NIntegrate[f[x],{x,x1,x2}]
 
(* Then set the endpoints of the steps, just as you did:*)

 xx = Table[-0.5 + (i -1)/(np-1), {i,1,np}];
 
(* Then partition into intervals:*)

Dxx = Partition[xx,2,1];
 
(* Set parameters:
 In[37]:= betaN = 121.643; n = 2;*)
 
(* Step through the intervals, accumulating the integral as we go:*)

FF = FoldList[#1 + DF[#2]&, 0, Dxx];
 
(* Plots of f and FF:*)

 In[39]:= ListPlot[{#,f[#]}&/@xx];
 In[40]:= ListPlot[Transpose[{xx,FF}]];
 



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