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

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Zig Herzog © 2014
Last revised: 08/23/13