For both methods
n = number of intervals ( must be even for Simpson's rule )
a = value of x at lower integration limit
b = value of x at upper integration limit
h = (b-a)/n = width of individual interval
xi = a + h*i for i=0 to i=n
f(xi) = value of function at x=xi
Trapezoidal Method
Area under straight line between xi and xi+1
Total area between x0=a and xn=b
Simpson's rule
Area under parabola of 2nd order connecting the points above xi ,
xi+1 and xi+2
Total area between x0=a and xn=b
Last revised: 08/23/13