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Mathematical integral
In the spherical coordinate system, the three line segment elements along the direction of the base vector are:

dl(r)=dr,dl(θ)=rdθ,dl(φ)=rsinθdφ

The bin area of spherical coordinates is:

dS=dl(θ)* dl(φ)=r^2*sinθdθdφ

The volume of the volume element is:

dv=dl(r)*dl(θ)*dl(φ)=r^2*sinθdrdθdφ