Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.: (a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z; 4π (b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd. 4π The integrals are over 4π. This is part of the derivation of the diffusion equation from the neutron transport equation. Part (b) from D&H Next note that the integral of the product of any odd number of components of OMEGA vanishes by symmetry. (a) I think that 4π/3 comes from the volume of the sphere and δij is the kronecker delta. I don't know how to show this mathematically. (b) I think that this has to do with the sin or cos function.