code for Simpson’s rule

Python code for Simpson’s rule

\\PMlinkescapetext{from math import *def f(x):  #function to integrate  return sin(x)def simpson_rule(a,b):  #Approximation by Simpson's rule  c=(a+b)/2.0  h=abs(b-a)/2.0  return h*(f(a)+4.0*f(c)+f(b))/3.0# Calculates integral of f(x) from 0 to 1print simpson_rule(0,1)}

Integrating $\sin x$ from $0$ to $1$ with the previous code gives $0.45986218971\mathrm{\dots }$ whereas the true value is $1-\cos 1=0.459697694131860282599063392557\mathrm{\dots }$.