By subsequently integrating L over the solid angle Ω Ω for all azimuthal angle (0 to 2 π π ) and polar angle θ θ from 0 to π π / 2 , we arrive at the Stefan–Boltzmann law : the power j * emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature: j ⋆ ⋆ = σ σ T 4 , We used ∫ ∫ cos ⁡ ⁡ θ θ d Ω Ω = ∫ ∫ 0 2 π π ∫ ∫ 0 π π / 2 cos ⁡ ⁡ θ θ sin ⁡ ⁡ θ θ d θ θ d ϕ ϕ = π π .