Approximation of integers and forming a table

function:

function y=func(x)
      y=sqrt(4−x^2);
end

The midpoint rule:

function y=Mid(a,b,N)
    dx=(b-a)/N;
    y=0;
    for i=1:N
        y=y+func(a+(i-0.5)*dx)*dx;
    end
end

The trapezoidal rule:

function y=Trap(a,b,N)
    dx=(b-a)/N;
    y=0;
    for i=1:N
        y=y+0.5*(func(a+(i-1)*dx) + func(a+i*dx))*dx;
    end
end

Simpson’s Rule:

function y=Simp(a,b,N)
    dx=(b-a)/N;
    y=0;
    for i=1:N
        y=y+(1/6)*(func(a+(i-1)*dx) + 4*func(a+(i-0.5)*dx) + func(a+i*dx))*dx;
    end
end

Question:

IN MATLAB ONLY

Using these four functions, create a script to publish, writing a cell that uses N=10,20,40,80,160,320 to calculate the approximations to the integral below using each of the three rules. The script should calculate the values as well as the absolute errors for each rule and display them in a nicely formatted table, which should include the method, N, the approximate value, and the absolute error. To format the table, use

fprintf('\%s | \%s | \%s | \%s \\n','N','Method','Value','AbsError')

Can't figure out how to run a loop for each different N and to put it in a table

[John D'Errico]

Please stop asking the same question, just to change ONE line of text, adding your question. You posted exactly the same information before.

[Benjamin Trivers]

its because i cant find my original post for this

[John D'Errico]

It was there. I've closed it now, because it added nothing, as a duplicate question.

Answer 1

[John D'Errico]

Just use a loop. You already seem to know how to use a loop.

a = ... % whatever
b = ... % whatever

Nlevels = [10,20,40,80,160,320];
for nind = 1:numel(Nlevels);
  N = Nlevels(nind);
  ymid_ind = Mid(a,b,N);
  
  fprintf(...)
end

You can do the same for each rule, looping over the various N.