Use spherical coordinates. evaluate xyz dv e , where e lies between the spheres ρ = 4 and ρ = 6 and above the cone ϕ = π/3.

Set

so that the volume element is

The integral is then

and so evaluates to 0.

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this