## Weddle's Method

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### Description

Weddle’s rule is a method of integration used for computing definite integral. The integral is calculated from a set of numerical values of the integrand. This method of integration is also known as mechanical quadrature.

DERIVATION

A mechanical quadrature formula will be called closed or open according to the limits of integration are used as interpolating points or not.

Sometimes it is easy to calculate the integration by breaking the whole interval into some subintervals. After computing each subinterval we have to add it to get the actual result.

By using newton cote’s formula we get,

Then,

Hence,

For n = 6,

The seven-point Newton-cotes closed type formula is:

And

GRAPHICAL REPRESENTATION

### Algorithm

INPUT:

A function f(x)

OUTPUT:

The value after integrating f(x) using Weddle's formula

PROCESS:

``````Step 1: [Defining the function f(x)]
Return 1/(1 + x^2)
[End of function f(x)]

Step 2: [Defining the function for performing weddle’s rule of integration]
Read x0, xn [the lower limit and upper limit]
Red n [number of intervals]
Set h ← (xn - x0)/n
If n Mod 6 = 0 then
Set s ← s+((3h/10)(f(x0)+f(x0+2h)+5f(x0+h)+6f(x0+3h)+f(x0+4h)+5f(x0+5h)+f(x0+6h)))
print s
else
print "The integration cannot be done using Weddle's Rule"
[End of ‘if’]
[End of ‘weddle’s’ rule]``````

### Code

1. It gives a more accurate solution than some other formulas.

2. Useful for solving the integrations which are difficult to perform mathematically.

APPLICATIONS

1. The result after calculating integral using this rule is more accurate than the other rules of computing Quadrature Formulas.

2. It is used for solving multiple integrals.

3. This rule is used to solve such integrations which can not be solved in closed form or are very difficult to solve the integration in closed form.