Plotting results of NIntegrate with variable integration limit

Question

I have tried to use NIntegrate with variable limits and compute the following

(*parameters*)
Ωm = 1.0;
ΩΛ = 0.0;
Ωk = 
  1 - Ωm - ΩΛ;

(*Integral with variable limits*)
 A[a_?NumericQ] := (5 Ωm)/
       2 ((Ωm a^-3 + ΩΛ + \
    Ωk a^-2)^(1/2)) NIntegrate[
        1/(x (Ωm x^-3 + ΩΛ + \
    Ωk x^-2)^(1/2))^3, {x, 10^-7, a}];

   (*plotting data giving values to `a`*)
  Plot2 = ListLinePlot[A[a], {a, 0.1, 1}, PlotRange -> {0, 1}, 
          AxesOrigin -> {0, 0}]

I supposed that A[a] was "free" until ListLinePlot give values to a, but no.

Another problem is that NIntegrate is not working here, the plot at the end looks like y=x.

Answer 1

You are almost there. You only missed to create the list that you want to plot. Here are your definitions:

  (*parameters*)
Ωm = 1.0;
ΩΛ = 0.0;
Ωk = 
  1 - Ωm - ΩΛ;

(*Integral with variable limits*)
A[a_?NumericQ] := (5 Ωm)/
    2 ((Ωm a^-3 + ΩΛ + \
Ωk a^-2)^(1/2)) NIntegrate[
    1/(x (Ωm x^-3 + ΩΛ + \
Ωk x^-2)^(1/2))^3, {x, 10^-7, a}];

Here is the list with the structure {a, int}:

  lst = Table[{a, A[a]}, {a, 0.1, 1, 0.05}]

and then one should plot the list, rather than the function:

 Plot2 = ListLinePlot[lst, PlotRange -> {0, 1}, AxesOrigin -> {0, 0}]

which returns the image below:

You could also do it as follows skipping the list stage:

Plot[A[a], {a, 0.1, 1}, PlotRange -> {0, 1}, AxesOrigin -> {0, 0}]

The returned image is identical to the one above.

Have fun!