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Re: plotting integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131703] Re: plotting integrals
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Sat, 21 Sep 2013 04:41:10 -0400 (EDT)
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Am Freitag, 20. September 2013 12:52:58 UTC+2 schrieb Herman:
> Dear All,
> 
> 
> 
> I would like to plot the function Subscript[\[Eta], B] but I got errors.
> 
> Could someone please help me with these errors?
> 
> 
> 
> 
> 
> \[Psi][x_, \[Omega]_] := (\[Omega]/\[Pi])^(1/4) 
> 
>   Exp[-1/2 \[Omega] x^2]
> 
> 
> 
> \[Psi]1[x_, a_, n_] := Sqrt[(2 n)!!/((2 n - 1)!! \[Pi])] Cos [a*x]^n
> 
> 
> 
> Subscript[F, TPT][x_, a_, n_] := 
> 
>  NIntegrate[\[Psi]1[x, a, n]*\[Psi][x, 
> 
>     a*Sqrt[2 n (n - 1)]], {x, -\[Pi]/2, \[Pi]/2}]
> 
> 
> 
> Subscript[\[Eta], B][x_, a_, 
> 
>   n_] := Sqrt[(1 - Subscript[F, TPT][x, a, n])]
> 
> 
> 
> Plot[Subscript[\[Eta], B][x, 1, 3], {x, -\[Pi]/2, \[Pi]/2}]

I don't understand why you still have the variable x which was integrated "away" in NIntegrate.

Ok, here is a piece of code very similar to yours which works.
Maybe it is close to what you intended ...

\[Psi][x_, \[Omega]_] := (\[Omega]/Pi)^(1/4)*
  Exp[(-2^(-1))*\[Omega]*x^2]
\[Psi]1[x_, a_, n_] := Sqrt[(2*n)!!/((2*n - 1)!!*Pi)]*Cos[a*x]^n
fTPT[a_, n_] := 
 NIntegrate[\[Psi]1[x, a, n]*\[Psi][x, a*Sqrt[2*n*(n - 1)]], {x, -Pi/
    2, Pi/2}]
etaB[a_, n_] := Sqrt[1 - fTPT[a, n]]
Plot[etaB[a, 3], {a, 0, 10}]

Best regards,
Wolfgang



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