SimpsonInt {asymmetry.measures} R Documentation

## Simpson integration

### Description

Implements simpson's extended integration rule.

### Usage

  SimpsonInt(xin,h)


### Arguments

 xin A vector of design points where the integral will be evaluated. h Assuming a

### Details

Simpson's extended numerical integration rule is implemented for n+1 equally spaced subdivisions (where n is even) of [a, b] as

\int_{a}^{b} f(x)\, dx = \frac{h}{3} ≤ft \{ f(a) + 4f(x_1) + 2f(x_2) + 4f(x_3) + 2f(x_4) + ... + 4f(x_{n-1}) + f(b)\right \}

where hx=(b-a)/n and x_i=a+ihx. Simpson's rule will return an exact result when the polynomial in question has a degree of three or less. For other functions, Simpson's Rule only gives an approximation.

### Value

A scalar, the approximate value of the integral.

### Author(s)

Dimitrios Bagkavos and Lucia Gamez Gallardo

R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com> , Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>

### Examples

x.in<- seq(0,pi/4,length=5)
h.out <- pi/8
SimpsonInt(x.in,h.out)


[Package asymmetry.measures version 0.2 Index]