Triple Integral for earth potensial

[keyos89]

Hi!
I am trying to solve this triple integral for computing the potential: G*ρ*∫∫∫-atan((x*y)/(z*sqrt(x^2+y^2+z^2)))dxdydz with the limits x = 0 to 1000 z = 0 to 1000 and z = 0 to 1. The G is tha gravitational constant and ρ is the density of rock/earth.
I have tried to use multiple softwares(matlab, maxima, wolframalpha) for solving this, but can't find any solutions. I am not sure of what I am doing wrong, can anyone help me?

Thanks!

 

[keyos89]

And i want the answar to be in mgal (milli gal)

 

[DimReg]

Your integrand choice seems a bit weird for the potential, are you sure this is the correct setup? Is this the potential of a slab of earth? or for the whole earth? (your bounds of integration are for the first case)

No one will know what is wrong with your attempts to use software unless you show what you input into the program.

 

[AlephZero]

If x and y are lengths, "atan(x*y)" doesn't make any sense. You can't take the inverse tangent of an area.

Maybe you meant atan(x/y)? Did you make the same mistake using Wolfram, etc?

 

[keyos89]

First, the formula for V_zz(potensial) has been given to me by my professor, the limits I use is for testing that I can compute the integral (but I can't...). I am supposed to solve a problem about how the masses around the gravimeter is working on it. I have measured the gradient in two different places, in the basement and one level up. I am supposed to get the same gradient and potensial when I move the gravimeter up from the basement (making a model). The formula is for computing the potensial of a prism.
The ρ-value is supposed to be 2670.

Okey, so this is how I try to do it in Maxima (just the inetgral, without the constants):
integrate(integrate(integrate(-atan((x*y)/(z*sqrt(x^2+y^2+z^2))),x,0,1000),y,0,1000),z,0,1);
But this will only compute the dx.

In MATLAB I am trying to use the integral3 function, like this:

f = @(x,y,z) (-atan((x.*y)./(z.*sqrt(x.^2+y.^2+z.^2))))

xmin = 0
xmax = 1000
ymin = @ (x) 0
ymax = @ (x) 1000
zmax = @ (x,y) 1
zmin = @ (x,y) 0

Q = integral3(f,xmin,xmax,ymin,ymax,zmin,zmax)

But this will have some dimensions porblems, so MATLAB won't execute.

I am not sure if I am supposed to make a bougerplate or if this is some kind of bougerplate?