trapz
Trapezoidal integration.
a=trapz(y)
a=trapz(x,y)
Inputs
x A vector.
y A vector of the same size as x if the latter is specified.
Outputs
a The integral of y obtained by the trapezoidal rule.


Description
If x is not specified, it is assumed to be the vector [0:n-1] where n is the size of y . The function returns the sum (y'*h)/2 where h[i]=x[i+1]-x[i-1] for 2<=i<=(n-1) , h[1]=(x[2]-x[1]) , and h[n]=(x[n]-x[n-1]) . This is, obviously, the implementation of the trapezoidal rule of integration.
Example
>>// Integral of sin(x) over [0,pi]=2.
>>x=[0:.02:1]'*pi
>>y=sin(x)
>>trapz(x,y) 
       1.9993
>>x=[0:.01:1]'*pi  //  Refined sampling
>>y=sin(x)
>>trapz(x,y)
       1.9998