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Matlab Approximate the Integral Assignment

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Hey Everyone! So I have an assignment that says to approximate the integral f(x)=e^(3x), -1<x<3. Answer the following questions

    Run the code with N=10, N=100, and N=1000.
    For each approximation, when does the result agree with the exact value of the integral to 4 digits?
    How much better is the trapezoidal rule than the other two? Explain this result using the theory given in the textbook and in lecture.


    2. Relevant equations

    I was given a sample code:The sample program below uses the left-endpoint rule, the right-endpoint rule and the trapezoid rule to approximate the definite integral of the function.

    f(x)=x^2, 0<x<1

    Matlab comments follow the percent sign (%)

    a= 0;
    b= 1;
    N = 10;
    h=(b-a)/N;
    x=[a:h:b]; %creates a vector of n+1 evenly spaced points
    f=x.^2;
    IL=0;
    IR=0;
    IT=0;
    for k=1:N; %Note that the vector f has (N+1) elements
    IL=IL+f(k);
    IR=IR+f(k+1);
    IT=IT+(f(k)+f(k+1))/2;
    end;
    IL=IL*h;
    IR=IR*h;
    IT=IT*h;

    fprintf(' When N = %i, we find:\n',N);
    fprintf(' Left-endpoint approximation = %f.\n',IL);
    fprintf('Right-endpoint approximation = %f.\n',IR);
    fprintf(' Trapezoidal approximation = %f.\n',IT);
    % Output from this program:
    When N = 10, we find:
    Left-endpoint approximation = 0.285000.
    Right-endpoint approximation = 0.385000.
    Trapezoidal approximation = 0.335000.


    3. The attempt at a solution

    I don't really have an idea to this. We were never taught it and I don't have any prior experience. What I got so far is a=-1;
    b=3;
    N=10;
    h=(b-a)/N;
    x=[a:h:b];
    f=e.^3x;
    Z = trapz(X,Y)

    Please help! Thanks in advance!
     
  2. jcsd
  3. Oct 22, 2012 #2

    uart

    User Avatar
    Science Advisor

    It looks like you're merely required to take the existing code and edit just the three lines where "a", "b" and "f" are defined.
     
  4. Oct 22, 2012 #3
    Yea, that's what I figured. Now I just have to find the actual answer somehow. I don't actually have Matlab, so that might be an issue lol.
     
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