Simpson’s Rule Integration软件

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

软件应用简介

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 

09/2010 (copyright Dr. Simpson)

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

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结果示意

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