solving multiple integrations
- To: mathgroup at smc.vnet.net
- Subject: [mg99941] solving multiple integrations
- From: sathyapaladugu at gmail.com
- 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 please help me to solve these integrals (remaining things such as Gamma .. are constants)