I need to take my trapezoid rule code and adjust it keeping the same format to Simpson rule

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Brady Wayne Robinson 2018-10-25

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回答： Paras Gupta 2024-6-21

I need to take my trapezoid rule code and adjust it keeping the same format to Simpson rule. I am just no sure how to get this done. I have tried this and keep getting errors. Here is my trapezoid code. Thank You so much! function s = myTrap(f,a,b,n) x = linspace(a,b,n+1); %for n trapezoids, use n+1 points h = (b-a)/n; s = (f(a)+f(b))/2; %initialize sum %trap sum for i = 2:n s = s + f(x(i)); end s = s*h; %multiply sum by h when f= @(x)sqrt(1+x^3) from 1-4 with 20 traps I get 12.875041 for simpson the same function 1-4 should output 12.871490

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Answer 1

Paras Gupta 2024-6-21

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Hello,

I understand that you want to adjust your trapezoid rule code to implement Simpson's rule while keeping the same format. Please refer to the following code to achieve the same in MATLAB:

f = @(x) sqrt(1 + x^3);
a = 1;
b = 4;
n = 20;
result = mySimpson(f, a, b, n);
fprintf('Result: %.6f\n', result);
Result: 12.871451
function s = mySimpson(f, a, b, n)
    if mod(n, 2) ~= 0
        error('n must be even for Simpson''s rule');
    end
    
    x = linspace(a, b, n+1); % for n intervals, use n+1 points
    h = (b - a) / n;
    s = f(a) + f(b); % initialize sum with f(a) and f(b)
    
    % Simpson's rule sum
    for i = 2:2:n
        s = s + 4 * f(x(i));
    end
    for i = 3:2:n-1
        s = s + 2 * f(x(i));
    end
    
    s = s * (h / 3); % multiply sum by h/3
end