# Newtons Cotes Quadrature Formula

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**Newton’s Cotes Quadrature Formula:**

Let where y = f (x) takes the values y_{0}, y_{1}, y_{2}, ...,y_{n} for x_{0}, x_{1}, x_{2}, ...,x_{n}. Let us divide the interval (a,b) into n equal parts of width h, so that;

Then

On substituting x = x_{0} 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.**