Newtons Cotes Quadrature Formula

Newton’s Cotes Quadrature Formula:

Let where y = f (x) takes the values y0, y1, y2, ...,yn for x0, x1, x2, ...,xn. Let us divide the interval (a,b) into n equal parts of width h, so that;




On substituting x = x0 rh, so that dx = hdr, we get


Now on integrating term by term, we get


Above Equation is known as Newton Quadrature Formula, which is also called as general qudrature formula.


Trapezodial Rule:

Setting n = 1 in the above equations, we obtain


For susequent intervals, similarly,


On adding all the above results,


which is known as Trepezodial Rule.