1.29 SICP

simpsons.scm

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
	 (sum term (next a) next b))))

(define (simpson-integral f a b n)
  (let ((h (/ (- b a ) n)))
  (define (term n)
    (define y (f (+ a (* h n))))
    (if (even? n)
	      (* 2 y)
	      (* 4 y)))
  (* (/ h 3) ; return
     (+ (f a)
	      (f b)
	      (sum term
	           1
	           (lambda (i) (+ i 1))
	           (- n 1))))))