By Simpson's 1 3 rd rule, the approximate value of the integral ₁^2 e^ -x / 2 d x using four intervals, is

Step-by-step solution

Given integral is ₁^2 e^ -x / 2 d x On dividing interval [1,2] in four parts, we have h= 2-1 4 = 1 4 Now, value of f(x)=e^ -x / 2 is given below array c|c|c|c|c|c x & 1 & 5 4 & 3 2 & 7 4 & e f(x) & 0.6065 & 0.5352 & 0.4724 & 0.4168 & 0.3679 array Now, Simpson's 1 3 rule is aligned _ x₀ ^ x₀+n h f(x) d x= & h 3 & [ (y₀+y_n )+4 (y₁+y₃+ +y_ n-1 ) . & .+2 (y₂+y₄+ +y_ n-2 ) ] aligned aligned ₁^2 e^ -x / 2 d x= & 1 12 [(0.6065+0.3679) & +4(0.5352+0.4168)+2(0.4724)] aligned aligned & = 1 12 [0.9744+3.808+0.9448] & = 1 12