ialan731
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Homework Statement
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.
Homework 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.
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!