Approximation of integers and forming a table

Question

Benjamin Trivers 2020-2-2

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/503285-approximation-of-integers-and-forming-a-table

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

3 个评论
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Benjamin Trivers 2020-2-2

its because i cant find my original post for this

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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Answer 1

John D'Errico 2020-2-2

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/503285-approximation-of-integers-and-forming-a-table#answer_413389

在 MATLAB Online 中打开

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