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Re: A problem with NIntegrate

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Dear Anna,

The imaginary part like here:

NIntegrate[((1 - (u/40)^2.5)*((1/((1 + 0.06*(u - t)))))/
       Exp[0.01*u*(1.5 - 1)])^(1/1.5), {u, t, 40}] /. t ->  0

NIntegrate::nlim: u = t is not a valid limit of integration.>>

19.7871 + 8.43907*10^-28 I

is the machine error. You should simply skip it. This can be easily done by the function Chop. Try this:

tab = Table[{t,
     NIntegrate[((1 - (u/40)^2.5)*((1/((1 + 0.06*(u - t)))))/
          Exp[0.01*u*(1.5 - 1)])^(1/1.5), {u, t, 40}]}, {t, 0, 40,
     1}] // Chop

{{0, 19.7871}, {1, 19.2601}, {2, 18.7278}, {3, 18.1903}, {4,
   17.6475}, {5, 17.0997}, {6, 16.5472}, {7, 15.99}, {8, 15.4286}, {9,
   14.8633}, {10, 14.2945}, {11, 13.7225}, {12, 13.1479}, {13,
   12.5712}, {14, 11.993}, {15, 11.4137}, {16, 10.8341}, {17,
   10.2548}, {18, 9.6765}, {19, 9.1001}, {20, 8.52637}, {21,
   7.95624}, {22, 7.39067}, {23, 6.83071}, {24, 6.27749}, {25,
   5.73225}, {26, 5.19632}, {27, 4.67117}, {28, 4.15839}, {29,
   3.65976}, {30, 3.17726}, {31, 2.71308}, {32, 2.26972}, {33,
   1.85006}, {34, 1.45742}, {35, 1.09575}, {36, 0.769879}, {37,
   0.485919}, {38, 0.252122}, {39, 0.0810213}, {40, 0}}

Then you get a nice smooth dependence of your integral upon t that could be easily approximated analytically, if needed. Play with this:

lstPl = ListPlot[tab, PlotStyle ->  Red];
ft = Fit[tab, {1, t, t^2, t^3}, t]
plFt = Plot[ft, {t, 0, 40}];
Show[{lstPl, plFt}]

Have fun, Alexei


Hi all,

I need to numerically integrate a function by utilizing =93Table=94 commandin
the process (please see the code below), but for the parameter values I am
interested in, I get complex results. I do not know why this is happening.
Also, how do I get "normal" real values instead, and also ensuring that the
answer is reasonably correct which one would expect from NIntegrate command.
Thanks a lot.

Table[NIntegrate[((1-(u/40)^2.5)*((1/((1+0.06*(u-t)))))/Exp[0.01*u*(1.5-1)])^(1/1.5),{u,t,40}],{t,0,40,1}]

-- 
Alexei Boulbitch, Dr. habil.
Senior Scientist
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Re: A problem with NIntegrate Alexei Boulbitch <alexei.boulbitch@iee.lu> - 2011-05-24 09:59 +0000

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