1.29.tex

\documentclass[a4paper,12pt]{article}
\usepackage{listings}
\lstset{language=Lisp}

\begin{document}
Here's the function's definition
\begin{lstlisting}
(define (simpson-integral f a b n)
  (define (iter k h sum)
    (cond ((= k n)
	   (/ (* h (+ sum (f b)))
	      3))
	  ((odd? k)
	   (iter (+ k 1)
		 h
		 (+ sum
		    (* (f (+ a (* k h)))
		       4.0))))
	  (else
	   (iter (+ k 1)
		 h
		 (+ sum
		    (* (f (+ a (* k h)))
		       2.0))))))
  (iter 1 (/ (- b a) n) (f a)))
\end{lstlisting}
The following evaluations give us
\begin{lstlisting}
(simpson-integral cube 0 1 100)
\end{lstlisting}
$\rightarrow$ 0.25
\begin{lstlisting}
(simpson-integral cube 0 1 1000)
\end{lstlisting}
$\rightarrow$ 0.25000000000000006

So the results are more accurate than those of the procedure
\lstinline!integral!.
\end{document}