By Simpson's rule, the value of ₁² d x x dividing the interval (1, 2) into four equal parts, is

Step-by-step solution

aligned h= 2-1 4 &= 1 4 Now, x₀ &=1, x₁=1+ 1 4 , x₂=1+2 1 4 , x₃ &=1+3 1 4 , x₄=1+4 1 4 aligned ie, aligned x₀ &=1, x₁=1.25, x₂=1.5, x₃ &=1.75, x₄=2 y₀ &=1, y₁=0.8, y₂=0.667, y₃ &=0.571, y₄=0.5 aligned Using Simpson's 1 3 rd rule aligned ₁² d x x =& 1 12 [(1+0.5)+4(0.8+0.571) &+2(0.667)] =& 1 12 [1.5+5.484+1.334] =& 1 12 [8.318]=0.6932 aligned