Simpson's One _ Third Rule
Simpson's One_Third Rule : Let us suppose that interval (a,b) be divided into n equal sub intervals such that a = x₀,x₁,.........,xₙ₋₁,xₙ = b We know from Newton's Forward Difference Interpolation formula that y = y₀+ sΔy₀+s(s-1)/2! Δ²y₀+s(s-1)(s-2)/3! Δ³y₀ + ................ .........(1) Where xₙ = x₀+nh and x= x₀+sh .......(2) Integrating both sides of equation (1) , between x₀ and xₙ we get xₙ xₙ ∫ y dx = ∫ (y₀+sΔy₀+s(s-1)/2! Δ²y₀ x₀ x₀ + s(s-1)(s-2)/3! Δ³y₀+........