The following is the code for evaluating a definite integral of a given function by a Numerical Method called Simpson’s 3/8th Rule.
//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.
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.
The following code snippet evaluates the integral of 1/(1+x^2) from 0 to 2.