SimpsonInt {asymmetry.measures}

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<b and n is a positive integer. h = (b-a)/n.

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} \left \{ 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 <[e-mail]> , Lucia Gamez Gallardo <[e-mail]>

References

Simpson's Rule

Examples

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