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MatLab Approximations

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data
    I need to answer the attached question, but we haven't done anything similar in class and the book isn't proving to be helpful for me. I'm not sure if I have to use matlab, we were given this code but I can't even understand what it is calculating.

    % f(x), the function to integrate
    % f= @(x) x^4-2*x ;
    % f= @(x) exp(x);
    f=@(x) sin(x);
    % a, the lower limit of integration
    a=0 ;
    % b, the upper limit of integration
    b=pi ;
    % b=1.0;
    % n, the number of segments. Note that this number must be even.
    % n=20 ;
    %**********************************************************************
    format long g
    h=(b-a)/n ;
    % Sum the odd index function values, and multiply by 4
    sumOdd=0 ;
    for i=1:2:n-1
    sumOdd=sumOdd+f(a+i*h) ;
    end
    % Sum the even index function values, and multiply by 2
    sumEven=0 ;
    for i=2:2:n-2
    sumEven=sumEven+f(a+i*h) ;
    end
    sum=4*sumOdd+2*sumEven+f(a)+f(b) ;
    % Then multiply by h/3
    approx=h/3*sum ;
    %exact = quad(f,a,b) ;
    %exact=exp(b)-exp(a);
    exact=-cos(b)-(-cos(a));
    error=abs(approx-exact);
    disp(approx);
    disp(exact);
    disp(error);

    Any help would be greatly appreciated!
     

    Attached Files:

  2. jcsd
  3. Oct 10, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It looks like a Simpson's rule approximation to the integral ##\int_0^{\pi} \sin(x) \, dx, ## using 20 equal intervals of length π/20. You are supposed also to compare the approximate and exact answers.

    Note: I am not a Matlab user and so am unfamiliar with all the syntax and commands, etc., but it is more-or-less obvious what this code is attempting.

    RGV
     
  4. Oct 11, 2012 #3
    Thank you for the help, but you don't need to make me feel bad for not understanding something you see is obvious. I do appreciate you pointing it out to me, I was having hard time seeing if it was the composite version.
     
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