You need to implement the simpson's rule on your own. A naive implementation would be something like that
f = @(t)t.^2;
N = 1000;
ti = 0;
tend = 5;
h=(tend-ti)/N;
t=linspace(ti,tend,N);
F = 0;
for i = 1:N-1
F = F + (h/6)*(f(t(i))+(4*f((t(i)+t(i+1))/2))+f(t(i+1)));
end
% To verify the result
AnalyticalResult = tend^3/3;
Error = (AnalyticalResult-F)/AnalyticalResult
Error =
1.0000e-03
