solving multiple integrations

• To: mathgroup at smc.vnet.net
• Subject: [mg99941] solving multiple integrations
• Date: Tue, 19 May 2009 07:01:48 -0400 (EDT)

```Hi
I have two integrals

u = Uth*2/\[Pi] Sqrt[1 + \[Gamma] Sin[m]^2]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(ArcSin[
\*FractionBox[\(Sin[\[Mu]]\), \(Sin[m]\)]]\), \(\[Pi]/2\)]\(
SqrtBox[
FractionBox[\(1 + \[Kappa]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)]\), \(\((1 + \[Gamma]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)*\((1 -
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)\)]] \[DifferentialD]x\)\);

\[Delta]= 2*\[Pi]*(ne*L)/\[Lambda]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(ArcSin[
\*FractionBox[\(Sin[\[Mu]]\), \(Sin[m]\)]]\),
FractionBox[\(\[Pi]\), \(2\)]]\(
SqrtBox[
FractionBox[\(\((1 + \[Kappa]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)*\((1 + \[Gamma]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)\), \(\((1 + \[Nu]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)*\((1 -
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)\)]] \[DifferentialD]x\)\)/\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(ArcSin[
\*FractionBox[\(Sin[\[Mu]]\), \(Sin[m]\)]]\),
FractionBox[\(\[Pi]\), \(2\)]]\(
SqrtBox[
FractionBox[\(\((1 + \[Kappa]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)*\((1 + \[Gamma]*
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)\), \((1 -
\*SuperscriptBox[\(Sin[m]\), \(2\)]*
\*SuperscriptBox[\(Sin[x]\), \(2\)])\)]] \[DifferentialD]x\)\) ;

i measure u and Delta from the experiment (u and delta are arrays)
kappa and mu are constants

I need to solve for kappa and mu using u and delta measured in
experiment