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RuleDelayed and Integration

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  RuleDelayed and Integration "Rob Y. H. Chai" <yhchai@ucdavis.edu> - 2011-05-03 09:47 +0000

#2060 — RuleDelayed and Integration

Hello everyone,

 

I wonder if I can get some help with three integrations below. Thanks.

 

Sincerely

 

Rob Chai

 

 

rules = {f[\[Epsilon]_] :>  

   Piecewise[{{0, \[Epsilon] <= 0}, {Es*\[Epsilon], 0 < \[Epsilon]}}]} 

 

\[Epsilon][x_, y_] := \[Epsilon]a + \[Phi]x*y + \[Phi]y*x  

 

eq1 = (Integrate[f[\[Epsilon][x, y]], {x, -b/2, b/2}, {y, -h/2, h/2}, 

     Assumptions -> {\[Epsilon]a, \[Phi]x, \[Phi]y, b, h, 

         Es} \[Element] Reals && b > 0 && h > 0 && Es > 0] == P) /. 

  Rules

 

eq2 = (Integrate[

     f[\[Epsilon][x, y]]*y, {x, -b/2, b/2}, {y, -h/2, h/2}, 

     Assumptions -> {\[Epsilon]a, \[Phi]x, \[Phi]y, b, h, 

         Es} \[Element] Reals && b > 0 && h > 0 && Es > 0] == Mx ) /. 

  rules

 

eq3 = (Integrate[

     f[\[Epsilon][x, y]]*x, {x, -b/2, b/2}, {y, -h/2, h/2}, 

     Assumptions -> {\[Epsilon]a, \[Phi]x, \[Phi]y, b, h, 

         Es} \[Element] Reals && b > 0 && h > 0 && Es > 0] == My) /. 

  rules 

 

soln = Solve[{eq1, eq2, eq3}, {\[Epsilon]a, \[Phi]x, \[Phi]y}]

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