If [2,6] is divided into four intervals of equal length, then the approximate value of ₂^6 1 x^2-x d x using Simpson's rule, is

Step-by-step solution

Here, h= 6-2 4 =1 Let, y= 1 x^2-x At x₀=2, y₀= 1 2^2-2 = 1 4-2 = 1 2 x₁=3, y₁= 1 3^2-3 = 1 6 x₂=4, y₂= 1 4^2-4 = 1 12 x₃=5, y₃= 1 5^2-5 = 1 20 x₄=6, y₄= 1 6^2-6 = 1 30 By Simpson's rule ₂^6 1 x^2-x d x= h 3 [y₀+y₄+4 (y₁+y₃ )+2 y₂ ]= 1 3 [ 1 2 + 1 30 +4 ( 1 6 + 1 20 )+2 1 12 ]= 1 3 [ 16 30 +4 26 120 + 1 6 ]= 1 3 16 30 + 26 30 + 5 30 = 16+26+5 90 = 47 90 =0.5222