RuleDelayed and Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg118578] RuleDelayed and Integration
- From: "Rob Y. H. Chai" <yhchai at ucdavis.edu>
- Date: Tue, 3 May 2011 05:47:46 -0400 (EDT)
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}]