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Topic: plotting integrals
Replies: 4   Last Post: Sep 24, 2013 4:16 AM

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Bob Hanlon

Posts: 892
Registered: 10/29/11
Re: plotting integrals
Posted: Sep 21, 2013 4:18 AM
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The definitions of Subscript[F,TPT] and Subscript[=E7,B] should not have th=
e
argument, x, since it is the variable of integration in the definition of
Subscript[F,TPT]. And presumably you want to plot with varying values of a.
Also, functions which use numerical techniques should have their arguments
restricted to numerical values.


=F8[x_, =F9_] := (=F9/=F0)^(1/4) Exp[-1/2 =F9 x^2];


=F81[x_, a_, n_] :=
Sqrt[(2 n)!!/((2 n - 1)!! =F0)] Cos[a*x]^n;


Subscript[F, TPT][a_?NumericQ, n_?NumericQ] :=
NIntegrate[
=F81[x, a, n]*=F8[x, a*Sqrt[2 n (n - 1)]],
{x, -=F0/2, =F0/2}];


Subscript[=E7, B][a_?NumericQ, n_?NumericQ] :=
Sqrt[(1 - Subscript[F, TPT][a, n])];


Plot[Subscript[=E7, B][a, 3],
{a, -.1, 2 Pi},
Frame -> True,
Axes -> False,
Exclusions -> 0]


Plot[Subscript[=E7, B][a, 3],
{a, 0, .01},
Frame -> True, Axes -> False,
Exclusions -> 0]



Bob Hanlon




On Fri, Sep 20, 2013 at 7:07 AM, Herman <btta2010@gmail.com> wrote:

> 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}]
>
>





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