(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: Matlab Approximate the Integral Assignment

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