Numerical Method - Old Questions

3. Derive Composite Simpson’s 1/3 Rule for numerical integration. How does it improve the accuracy of integration?

Here, the integration interval is divided into n number of segments of equal width, where n is even number. Then the step size is

We have from simpson’s 1/3 rule,

Therefore,

This equation is called composite Simpson’s 1/3 rule.

It improves the accuracy of integration formulae by locating integration points in special locations.