       Determination of a double integral

• To: mathgroup at smc.vnet.net
• Subject: [mg36873] Determination of a double integral
• From: Sven Richter <Sven.Richter at unibw-muenchen.de>
• Date: Mon, 30 Sep 2002 03:03:22 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hallo,

I have the problem, that I want to determine the numerical solution of a
double integral, like e.g. the following:

<< Statistics`ContinuousDistributions`
ndist = NormalDistribution[0, 1];

N[Sigma^2/(Abs[Mu_1^2 - Mu_2^2]) Integrate[(Integrate[1/y_1 1/(y - y_1)
PDF[ndist, d*Log[y_1] + c*Log[y - y_1] + f]*
PDF[ndist, Sigma*(c*Log[y_1] + d*Log[y - y_1] + g)], {y_1,0,y}]),
{y,0,Lambda}]]

whereby

Lambda := 3;
Mu_1 := 4;
Mu_2 := 5;
Sigma := 0.25;
a = 1/2 (Mu_1^2 + Mu_2^2/Sigma^2)
b = 1/2 (Mu_2^2 + Mu_1^2/Sigma^2)
c = -Mu_2/(Mu_1^2 - Mu_2^2)
d = -Mu_1/(Mu_2^2 - Mu_1^2)
f = d*a + c*b
g = c*a + d*b

Sorry for the poor code...

The problem is, that Mathematica doesn't give me a result (after waiting 2
hours I turned my machine off).
Thus, the question is, if there is still a possibility of solving such
complicated expressions...

TIA,
Sven.

```

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