We now establish a triple integral in the spherical coordinate system, as we did before in the cylindrical coordinate system. Let the function f(ρ,θ,φ)f(ρ,θ,φ)f(\rho,\theta,\varphi) be continuous in a bounded spherical box, B={(ρ,θ,φ)|a≤ρ≤b,α≤θ≤β,γ≤φ≤ψ}B={(ρ,θ,φ)|a≤ρ≤b,α≤θ≤β,γ≤φ≤ψ}B = \{(\rho,\theta,\varphi) | a \leq \rho \leq b, \, \alpha \leq \theta \leq \beta, \, \gamma \leq \varphi \leq \psi \}. We then divide each interval into l,m,nl,m,nl,m,n and nnn subdivisions such that Δρ=b−al,Δθ=β−αm.Δφ=ψ−γnΔρ=b−al,Δθ=β−αm.Δφ=ψ−γn\Delta \rho = \frac{b - a}{l}, \, \Delta \theta = \frac{\beta - \alpha}{m}. \, \Delta \varphi = \frac{\psi - \gamma}{n}. Now we can illustrate the following theorem for triple integrals in spherical coordinates with (ρ∗ijk,θ∗ijk,φ∗ijk)(ρijk∗,θijk∗,φijk∗)(\rho_{ijk}^*, \theta_{ijk}^*, \varphi_{ijk}^*) being any sample point in the spherical subbox BijkBijkB_{ijk}. For the volume element of the subbox ΔVΔV\Delta V in spherical coordinates, we have ΔV=(Δρ)(ρΔφ)(ρsinφΔθ)ΔV=(Δρ)(ρΔφ)(ρsinφΔθ)\Delta V = (\Delta \rho)\, (\rho \Delta \varphi)\, (\rho \, \sin \, \varphi \, \Delta \theta), as shown in the following figure.