## 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"))