Hi! My problem is the following: I have the following matrix:
S={{0,-z,y},{z,0,-x},{-y,0,x}}}
The integral of this matrix over any symmetric domain is 0. However, the integral of S^2
is not zero over a symmetric domain. I do not know what this domain is! I want to do the following:
Integrate[f[S,S^2],x,y,z]
Where f[S,S^2]
is a function I got from previous calculations that is very complicated and may have a bunch of S
and S^2
terms here and there. I want Mathematica to do the simplification for me and eliminate automatically integrals of terms with just S
in them, and keep integrals with S^2
terms.
I understand that this is what Mathematica is made for. I want to intervene as little as possible and make Mathematica do the simplification work - if I have to go through and manually set terms with just S
to zero in a 10-line expression, the point of the software becomes useless. Please help me on this! I really appreciate it.