What is Simpson Rule and its details ?

y =  (a₀ + a₁x +  a₂x²)

 where a₀, a₁ and a₂ are constants.

ln its simplest form, this rule states:-

The area between any three consecutive  ordinates is equal to the sum of  the end ordinates,plus four times the middle ordinate, all multiplied by one third of the common interval.

Let the curve in Figure, be a parabola of the second order. Let y1, y2 and y3 be three ordinates equally spaced at ‘h’ units apart. The area of the elementary strip is y dx.Then the area enclosed by the curve and the axes of reference is given by:

Simpson’s Second Rule:-

This rule assumes that the equation of the curve is of the third order, i.e. of a curve whose equation, referred to the co-ordinate axes, is of the form