sintegral {Bolstad2}

Numerical integration using Simpson's Rule

Description

Takes a vector of x values and a corresponding set of postive f(x)=y values and evaluates the area under the curve:

\int{f(x)dx}

.

Usage

sintegral(x, fx, n.pts = 256)

Arguments

x

a sequence of x values.

fx

the value of the function to be integrated at x.

n.pts

the number of points to be used in the integration.

Value

returns a list with the following elements

x

the x-values at which the integral has been evaluated

y

the cummulative integral

int

the value of the integral over the whole range

Examples

## integrate the normal density from -3 to 3
x=seq(-3,3,length=100)
fx=dnorm(x)
estimate=sintegral(x,fx)$int
true.val=diff(pnorm(c(-3,3)))
cat(paste('Absolute error :',round(abs(estimate-true.val),7),'\n'))
cat(paste('Relative percentage error :', 100*round((abs(estimate-true.val)/true.val),6),'%\n'))