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Mathematics Calculus Wolfram Language Numerical Computation

Writing power to an integral?

M M

Posted 1 year ago

Hello everybody. I have this integral: 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. Attachments: Untitled-10.nb

POSTED BY: M M

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 year ago

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}]

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}]

POSTED BY: Gianluca Gorni