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### Highlights from Simpson's Rule Integration

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# Simpson's Rule Integration

### Juan Camilo Medina (view profile)

16 Sep 2010 (Updated )

Computes an integral "I" via Simpson's rule in the interval [a,b] with n+1 equally spaced points

File Information
Description

This function computes the integral "I" via Simpson's rule in the interval [a,b] with n+1 equally spaced points

Syntax: I = simpsons(f,a,b,n)

Where,
f= can either be an anonymous function (e.g. f=@(x) sin(x)) or a vector containing equally spaced values of the function to be integrated
a= Initial point of interval
b= Last point of interval
n= # of sub-intervals (panels), must be integer

Written by Juan Camilo Medina - The University of Notre Dame

Example 1:

Suppose you want to integrate a function f(x) in the interval [-1,1].
You also want 3 integration points (2 panels) evenly distributed through the
domain (you can select more point for better accuracy).
Thus:
f=@(x) ((x-1).*x./2).*((x-1).*x./2);
I=simpsons(f,-1,1,2)

Example 2:

Suppose you want to integrate a function f(x) in the interval [-1,1].
You know some values of the function f(x) between the given interval,
those are fi= {1,0.518,0.230,0.078,0.014,0,0.006,0.014,0.014,0.006,0}
Thus:
fi= [1 0.518 0.230 0.078 0.014 0 0.006 0.014 0.014 0.006 0];
I=simpsons(fi,-1,1,[])
note that there is no need to provide the number of intervals (panels) "n",
since they are implicitly specified by the number of elements in the vector fi

Acknowledgements

This file inspired Simpson's 1/3 And 3/8 Rules and Simpson Quadrature.

MATLAB release MATLAB 7.10 (R2010a)
11 Feb 2014 Maxime Boudreau

### Maxime Boudreau (view profile)

Could it be possible that the algorithm isn't complete if n is odd? In that case, I think the formula doesn't take the last subinterval into account.

To see it, you can try:
simpsons(@sin,0,pi,100)
simpsons(@sin,0,pi,101)
simpsons(@sin,0,pi,102)
...

Comment only
09 Sep 2012 Ivan

06 Jun 2011 shin

### shin (view profile)

goddd

Comment only
02 Nov 2010 Juan Camilo Medina

Comment only
22 Sep 2010 1.1

n/a

29 Sep 2010 1.2

.

01 Nov 2010 1.3

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08 Apr 2011 1.4