simpson's 3/8 rule in matlab

Simpson's 3/8 rule can be used for numerical integration. Here is a matlab code to do so:

main.m
function I = simpson38_rule(f, a, b)
% f : function to be integrated
% a, b : limits of integration

h = (b-a)/3;
I = h*(f(a) + 3*f(a+h) + 3*f(a+2*h) + f(b));
end
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To use the above function for numerical integration, simply pass the function that needs to be integrated, and the limits of integration as inputs to the function. The output will be the numerical approximation of the integral.

For example, let's say we want to find the numerical approximation of the integral of sin(x) from 0 to pi/2. We can call the simpson38_rule function as follows:

main.m
>> I = simpson38_rule(@(x) sin(x), 0, pi/2)
I =

    0.999839171711558
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Therefore, the numerical approximation of the integral of sin(x) from 0 to pi/2 using Simpson's 3/8 rule is approximately 0.9998.