double integral of long expression in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg80868] double integral of long expression in Mathematica
• From: negedea at googlemail.com
• Date: Tue, 4 Sep 2007 06:35:10 -0400 (EDT)

```Dear All,

Please if anyone knows how to evaluate the following two double
integrals (see below: Int1 = f1 f2 f3 f4 and Int2 = f1 f2 f3 f5 )
inMathematica. Preferebily in a closed for otherwise approximate
method could also work. I have tried the Integrate command by
separating variables and also on the entire equation but failed.

The inputForm is also included in the body of the email.

Please!,

negede

In[34]:=
f1 = 1/(3*E^((-42.13+=CF=842)^2/18)*Sqrt[2*Pi]);
f2= (5.778367760333042*^-19*(11.12+=CF=843)^12.13)/
E^(4.4008893833458054*^-20*(11.\
12+=CF=843)^13.13);
f3 = Abs[Cot[0.017453292519943295*=CF=842]];
f4=0.0037739313253375532/
E^(0.000044744314476429635*(449.96310600570723-55.\
69524532558123*=CF=843+1.*=CF=84*Cot[0.017453292519943295*=CF=842])^2);
f5=
(7.133612341840616*^-13*(-18.963106005707232+55.69524532558123*=CF=843-1.*=
=CF=84*
\
Cot[0.017453292519943295*=CF=842])^3.8)/E^(1.4861692378834617*^-13*(-18.\
963106005707232+55.69524532558123*=CF=843-1.*=CF=84*Cot[0.01745329251994329=
5*=CF=842])^4.8);

In[39]:=
Int1=f1 f2 f3 f4 //FullSimplify//InputForm

Out[39]//InputForm=
2=2E899933125405506*^-22*
E^(-0.05555555555555555*(-42.13 + =CF=842)^2 -
4.4008893833458054*^-20*(11.12 + =CF=843)^13.13 -
0.000044744314476429635*(449.96310600570723 -
55.69524532558123*=CF=843 +
1.*=CF=84*Cot[0.017453292519943295*=CF=842])^2)*
(11.12 + =CF=843)^12.13*
Abs[Cot[0.017453292519943295*=CF=842]]

In[40]:=
Int2=f1 f2 f3 f5 //FullSimplify//InputForm

Out[40]//InputForm=
5=2E481551451404547*^-32*
E^(-0.05555555555555555*(-42.13 + =CF=842)^2 -
4.4008893833458054*^-20*(11.12 + =CF=843)^13.13 -
1.4861692378834617*^-13*(-18.963106005707232 +
55.69524532558123*=CF=843 -
1.*=CF=84*Cot[0.017453292519943295*=CF=842])^4.8)*
(11.12 + =CF=843)^12.13*
Abs[Cot[0.017453292519943295*=CF=842]]*
(-18.963106005707232 + 55.69524532558123*=CF=843 -
1.*=CF=84*Cot[0.017453292519943295*=CF=842])^3.8

Integrate[Int1,{=CF=842,35,50},{=CF=843,10,23}]

Integrate[Int1,{=CF=842,35,50},{=CF=843,10,23}]

```

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