The following is the code for evaluating a definite integral of a given function by a Numerical Method called Simpson’s 3/8th Rule.

**DOWNLOAD**:simpson2

//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**.

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

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