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}]];