Approximation of integers and forming a table

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Benjamin Trivers
Benjamin Trivers 2020-2-2
回答： John D'Errico 2020-2-2
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
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John D'Errico
John D'Errico 2020-2-2
It was there. I've closed it now, because it added nothing, as a duplicate question.

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回答（1 个）

John D'Errico
John D'Errico 2020-2-2
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.

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