//Simpson's 3/8th Rule
//Evaluates the definite integral of a function f(x), from a to b.
//Written By: Manas Sharma(www.bragitoff.com)
funcprot(0);
function ans=simpson2(a,b,n,f)//function definition of simpson
h=(b-a)/n;
sum=0;
for i=1:n-1
x=a+i*h;
if modulo(i,3)==0
sum=sum+2*f(x);
else
sum=sum+3*f(x);
end
end
ans=(3*h/8)*(f(a)+f(b)+sum);
endfunction
//NOTE: When the function is called the value of the third argument that is, n, should be a multiple of 3.

You can either copy the code above and save it as a .sci file or download the file . Once you run the code, the function ‘simpson2(a,b,n,f)’ can be called by other programs or even in the console.

Function syntax:

simpson2(a,b,n,f)

where,

a=initial limit(real no.) b=final limit(real no.) n=no. of sub-intervals(the higher the value of ‘n’ the better is the result. NOTE: n should be a multiple of 3.

Example:
The following code snippet evaluates the integral of 1/(1+x^2) from 0 to 2.

PhD researcher at Friedrich-Schiller University Jena, Germany. I'm a physicist specializing in theoretical, computational and experimental condensed matter physics. I like to develop Physics related apps and softwares from time to time. Can code in most of the popular languages. Like to share my knowledge in Physics and applications using this Blog and a YouTube channel.