We assume that the triple integral I= ∫∫∫ f(x,y,z) dx dy dz can be very useful in many situations, the simplest of which is mass calculation with non-uniform density.
If the total mass M is distributed over a volume, we can represent how this mass is distributed with a function f(x,y,z) which gives the density at the point (x,y,z).
If you integrate over volume, you can calculate the total mass.
the triple integral I = ∫∫∫ f(x,y,z) dx dy dz can be used for mass calculation with non-uniform density, among other best applications.
But mass calculation is a short-sighted application.
In fact This triple integral I= ∫∫∫ f(x,y,z) dx dy dz
is one of the best tools for testing the correctness of proposed spaces.
This can show the importance of the topic of 4D x-t spaces.
the triple integral I= ∫∫∫ f(x,y,z) dx dy dz shows that Minkowski space-time (sometimes called event space), which is incomplete and even misleading, is only a modest attempt to describe the space of special events. events. relativity,.
He cannot evaluate the triple integral or even define it!
Pseudospaces such as Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, are not the best choice.
On the other hand, the full 4D unit space of matrix B strings can do the job.
Ismail Abbas M. Abbas A triple integral is used to calculate the volume of a three-dimensional region or the total quantity of a function over a three-dimensional space. It is commonly applied in fields like physics, engineering, and mathematics to find quantities such as mass, charge, or fluid flow within a given volume, especially when the function being integrated varies with position within that volume. It can also be used for computing the center of mass and other related properties in 3D.
The triple integral I= ∫∫∫(on the domain V) f(x,y,z) dV cannot be calculated either analytically in the general case or even numerically.
Recently we have seen many attempts, some using the Schrödinger equation in QM!?, to evaluate its integral, but unfortunately all ended in failure.
Perhaps this is why Einstein introduced tensor algebra just to estimate the total garavity energy near the sun, as follows:
U= ∫∫∫ G(x,y,z) dx dy dz
.
To our knowledge the only numerical method we know for this triple integral is [1],
i= f(x1,y1,z1) . SW1 +f(x2,y2,z2) . SW2. . . + f(x27,y27,z27) . SW27
Where SW,s are the statistical weights of the triple integral.
Numerical examples,
I=∫∫∫[0,1]^3 f(x,y,z) dx dy dz
for f(x)=x or f(x)=y or f(x)=z
then I is almost the same and is equal to 13.6
for f(x)=x^2 or f(x)=y^2 or f(x)=z^2
then I have almost the same value and equals 11
for f(x)=x+y+z,
I = 40.54
1- A rigorous reform of physics and mathematics.
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