Writing power to an integral?

Questions
,
1

Hello everybody.

I have this integral:

88.PNG

I used this code:

NIntegrate[
 Subscript[\[Lambda], 2][s, u] Vbar[u], {s, 
  0, T},{u, 0, s}]

How can I put the ‘2’ power?

I tried this code:

NIntegrate[
 NIntegrate[Subscript[\[Lambda], 2][s, u] Vbar[u], {u, 0, s}]^2, {s, 
  0, T}]

This code gives me an answer but it has an error. How can I solve this error?

I attached the code as well.
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=88.PNG&userId=2589518

Untitled-10.nb (17.8 KB)

2

Perhaps like this ( I think you should avoid complcated varable-names)

NIntegrate[(Integrate[ lam2[s,u] Vbar[u],{u,0,s}])^2,{s,0,T}]
3

To eliminate the square I am afraid you will need to go to a triple integral:

Integrate[Integrate[f[s, u], {u, 0, s}]^2, {s, 0, T}] ==
 Integrate[Integrate[f[s, u], {u, 0, s}]*
   Integrate[f[s, v], {v, 0, s}],
  {s, 0, T}] ==
 Integrate[Integrate[f[s, u] f[s, v], {u, 0, s}, {v, 0, s}],
  {s, 0, T}] ==
 Integrate[f[s, u] f[s, v], {s, 0, T}, {u, 0, s}, {v, 0, s}]
4

Thank you.

It works correctly.