       Problem with Integral in mathematica 5.1

• To: mathgroup at smc.vnet.net
• Subject: [mg82493] Problem with Integral in mathematica 5.1
• From: cyrius24 <cyrilschamper at hotmail.com>
• Date: Mon, 22 Oct 2007 05:39:12 -0400 (EDT)

```Hi,

I have three integrals on a volume which normaly gives the same value when I make the integral on a cubic volume (same intervals for the three variables). In the starting functions which all depend on x,y and z, there is just a change in the numerator, it is x^2 for Gxx, y^2 for Gyy, and z^2 for Gzz. I obtain the same results at the end for Gxx and Gzz, but Gyy is different. And I actually don't understand. Below I paste the three different scripts for Gxx,Gyy, and Gzz. If you find something strange, please tell me.

Best regards

Gxx:

f[x_, y_, z_] = 1/(4*Pi*yc)*(3*
x^2/(Sqrt[x^2 +
y^2 + z^2])^5 - 1/(
Sqrt[x^2 + y^2 + z^2])^3 + k^2/2*(x^2/(Sqrt[x^2 + y^2 +
z^2])^3 + 1/(Sqrt[x^2 + y^2 + z^2])));
g[x_, y_, z_] = Integrate[f[x, y, x], x];
h[y_, z_] = g[x2, y, z] - g[x1, y, z];
i[y_, z_] = Integrate[h[y, z], y];
j[z_] = i[y2, z] - i[y1, z];
l[z_] = Integrate[j[z], z];
res = l[z2] - l[z1] // FortranForm
x1 = -0.5;
x2 = 0.5;
y1 = -0.5;
y2 = 0.5;
z1 = -0.5;
z2 = 0.5;
yc = 1 + I*5.56*10^(-11);
k = 1.99*10^(-3) - I*1.99^(-3);
res

Gyy:

f[x_, y_, z_] = 1/(4*Pi*yc)*(3*
y^2/(Sqrt[x^2 +
y^2 + z^2])^5 - 1/(
Sqrt[x^2 + y^2 + z^2])^3 + k^2/2*(y^2/(Sqrt[x^2 + y^2 +
z^2])^3 + 1/(Sqrt[x^2 + y^2 + z^2])));
g[x_, y_, z_] = Integrate[f[x, y, x], x];
h[y_, z_] = g[x2, y, z] - g[x1, y, z];
i[y_, z_] = Integrate[h[y, z], y];
j[z_] = i[y2, z] - i[y1, z];
l[z_] = Integrate[j[z], z];
res = l[z2] - l[z1] // FortranForm
x1 = -0.5;
x2 = 0.5;
y1 = -0.5;
y2 = 0.5;
z1 = -0.5;
z2 = 0.5;
yc = 1 + I*5.56*10^(-11);
k = 1.99*10^(-3) - I*1.99^(-3);
res

Gzz:

f[x_, y_, z_] = 1/(4*Pi*yc)*(3*
z^2/(Sqrt[x^2 +
y^2 + z^2])^5 - 1/(
Sqrt[x^2 + y^2 + z^2])^3 + k^2/2*(z^2/(Sqrt[x^2 + y^2 +
z^2])^3 + 1/(Sqrt[x^2 + y^2 + z^2])));
g[x_, y_, z_] = Integrate[f[x, y, x], x];
h[y_, z_] = g[x2, y, z] - g[x1, y, z];
i[y_, z_] = Integrate[h[y, z], y];
j[z_] = i[y2, z] - i[y1, z];
l[z_] = Integrate[j[z], z];
res = l[z2] - l[z1] // FortranForm
x1 = -0.5;
x2 = 0.5;
y1 = -0.5;
y2 = 0.5;
z1 = -0.5;
z2 = 0.5;
yc = 1 + I*5.56*10^(-11);
k = 1.99*10^(-3) - I*1.99^(-3);
res

```

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