By the application of Simpson's one-third rule for numerical integration, with two subintervals, the value of ₀¹ d x 1+x is

Step-by-step solution

Since, the given integration is divided into two subintervals. ie, h= 1-0 2 = 1 2 ₀¹ 1 1+x d x= h 3 [ (y₀+y₂ )+4 (y₁ ) ] At aligned x=0, y &=1 x &= 1 2 , y₁= 2 3 aligned and x=1, y₂= 1 2 aligned ₀¹ 1 1+x d x &= 1 2 3 [ (1+ 1 2 )+4 ( 2 3 ) ] &= 1 6 [ 3 2 + 8 3 ]= 25 36 aligned