# Simpsom's 3/8 Rule

In the general case, the bound for the error expression is given by

where,

If f(x) is a polynomial of degree ≤ 3, then f (4) (x) = 0. This result implies that error expression given in (3.47) or (3.48) is zero and the composite Simpson’s 3/8 rule produces exact results for polynomials of degree ≤ 3. Therefore, the formula is of order 3, which is same as the order of the Simpson’s 1/3 rule.

**Note :
**

1. In Simpson’s 3/8th rule, the number of subintervals is n = 3N. Hence, we have

where n is a multiple of 3.

2. Simpson’s 3/8 rule has some disadvantages. They are the following: (i) The number of subintervals must be divisible by 3. (ii) It is of the same order as the Simpson’s 1/3 rule, which only requires that the number of nodal points must be odd. (iii) The error constant c in the case of Simpson’s 3/8 rule is c = 3/80, which is much larger than the error constant c = 1/90, in the case of Simpson’s 1/3 rule. Therefore, the error in the case of the Simpson’s 3/8 rule is

larger than the error in the case Simpson 1/3 rule. Due to these disadvantages, Simpson’s 3/8 rule is not used in practice