Simpson 3/8 Rule

Simpson’s 3/8 Rule:

Setting n = 3 in Newton’s Cotes Quadrature Formula, we obtain

For susequent intervals, similarly,

On adding all the above results,

which is known as Simpson’s 3/8 Rule.

Example: Evaluate I using Simpson’s 3/8 rule.

Solution: Here we have;

where xin[0,6] Consider 6 intervals, thus

By using this information, we may prepare the following table:

By Simpson rule (for 7 values);