1. The problem statement, all variables and given/known data Hi folks, I am sure this is very simple but there are not enough steps given in this calculation for my simple brain to get from the beginning to the end! σ = ∫ (dσ/dΩ) = ∫ r2sin2θ (no integral limits given) σ = 2∏r2 ∫ (1 - u2) du (integral from -1 to 1) σ = 8∏r2 / 3 2. Relevant equations u = cos θ 3. The attempt at a solution I used Ω = sin θ dθ d∅ and first integrated ∅ from 0 to 2∏ to get σ = ∫ dσ = r2 ∫ sin2θ dΩ σ = 2∏ r2 ∫ sin2θ sin θ dθ Use sin2θ = 1 - cos2θ to get σ = 2∏ r2 ∫(1 - cos2θ) sin θ dθ Let u = cos θ so du/dθ = - sin θ and dθ = -arcsin θ to get σ = 2∏ r2 ∫(1 - u2) sin θ -arcsin θ du I think sin and arcsin cancel to give σ = 2∏ r2 -∫(1 - u2) du σ = 2∏ r2 2u From the answer that was given I have the integral limits running from -1 to 1 so the final term becomes [2 - (-2)] = 4 which gives σ = 8∏ r2 Where am I going wrong please?