Maths for Engineers - 3

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;

 

Then

              

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.