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!