### Simpson's Rule

**Approximate evaluation of a definite integral :**

**Simpson's Rule .**

In many cases , a definite integral can not be obtained either because the quantity to be integrated can not be expressed as a mathematical function , or because the indefinite integral of the unction itself can not be determined directly . In such cases formula of approximation are used . One such important formula is

**Simpson's Rule**. By this rule the definite integral of any function is expressed in terms of the individual values of any number of ordinates within the interval , by assuming that the function within each of the small ranges into which the whole interval may be divided can be represented to a sufficient degree of approximation by a parabolic function .

In numerical analysis,

**Simpson's rule**is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation:

Suppose that the interval is split up in subintervals, with an even number. Then, the composite Simpson's rule is given by

In other words this

**Simpson's Rule**can be written as :

**h/3 [sum of the extreme ordinates + 2.sum of the remaining odd ordinates + 4.sum of the even ordinates]**

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