How to plot a function for various values of 2 constants

Question

I have a function like this:

f[x_, ψ_, δ_] := 
 Flatten[Table[{k, 
    1 + (E^(-(x^2/(2 δ^2))) x^2 ψ)/δ^4 - (
     E^(-(x^2/(2 δ^2))) ψ)/δ^2 - (
     0.19947114020071635` Gamma[
       1 + k] ((
        Sqrt[2 π] Gamma[-(3/2) + k])/((1/(-3 + 2 k))^(3/2)
          Gamma[k]) - 
        8 Sqrt[E^(-(x^2/(2 δ^2))) ψ]
          Hypergeometric2F1[1/2, k, 3/2, (
          2 E^(-(x^2/(2 δ^2))) ψ)/(3 - 2 k)]))/(
     k Sqrt[-3 + 2 k] Gamma[-0.5` + k])}, {k, {2, 400}}]]

In this I have two constants ψ and δ. Now I need to integrate this function different values of \psi and \delta. For each ψ , the delta will vary from 1,10. So for each ψ , I need to plot output.

Now for a single value of \psi, I can write as

ψ=0.4;
p1 = 
 Table[{δ, 
   NIntegrate[f[x, ψ,δ][[2]], {x, -50, 50}]}, {δ, 1, 10, 
   0.1}]

and plot the output

In a similar way I need to plot for 6 more values of ψ and make a subplot of 6 plots.

Thanks in advance.

Answer 1

ψlist = Range[.3, .6, .3/5];
δlist[ψ_] := Range[##, (#2 - #)/10] & @@ ψ {.75, 1.25};
pts = Table[{δ, NIntegrate[f[x, ψ, δ][[2]], {x, -50, 50}]}, {ψ, ψlist}, {δ, δlist[ψ]}];

ListLinePlot[pts, PlotLegends -> ("ψ = " <> ToString[#] & /@ ψlist),
 AxesLabel -> {δ, TraditionalForm @ HoldForm @ Integrate[f[x, ψ, δ][[2]], {x, -50, 50}]}]

Answer 2

Something like this?

p1[ψ_] := 
  Table[{δ, 
    NIntegrate[f[x, ψ, δ][[2]], {x, -50, 50}]}, {δ,
     1, 10, 0.1}];

Table[ListPlot[p1[ψ]], {ψ, {1, 2, 3, 4, 5, 6}}]