Introduction to Closed Newton - Cotes Formulae
Newton – Cotes formulae use interpolating polynomials toto evaluateusing leading to the formulawhere theare equally spaced, so
The simplest example of this method is the trapezium rule. It calculates the area of the trapezium formed by approximatingusing linear interpolation. This is shown below forthat interpolates onlyand
The trapezium rule can be obtained by integrating the linear interpolation function
over the interval
We can generate other integration rules by using higher order Lagrange polynomials.
Theare labelledand called weights, thus we obtain
Closed Newton – Cotes formulae include the endpointsandin the interpolating polynomial.