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);
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
Hope this helps.
