65D32-CodeForSimpsonsRule.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{CodeForSimpsonsRule}
\pmcreated{2013-03-22 14:50:52}
\pmmodified{2013-03-22 14:50:52}
\pmowner{drini}{3}
\pmmodifier{drini}{3}
\pmtitle{code for Simpson's rule}
\pmrecord{7}{36518}
\pmprivacy{1}
\pmauthor{drini}{3}
\pmtype{Algorithm}
\pmcomment{trigger rebuild}
\pmclassification{msc}{65D32}
\pmrelated{NewtonAndCotesFormulas}

\endmetadata

\usepackage{graphicx}
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\newcommand{\figuraex}[2]{\begin{center}\includegraphics[#2]{#1}\end{center}}
\newtheorem{dfn}{Definition}
\begin{document}
\textbf{Python code for Simpson's rule}

\begin{verbatim}
\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 1
print simpson_rule(0,1)
}
\end{verbatim}

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