SICP 习题1. 29 simpson 积分

(define (cube x)
  (* x x x))

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

(define (integral f a b dx)
  (define (add-dx x) (+ x dx))
  (* (sum f (+ a (/ dx 2.0)) add-dx b) dx))

(newline)
(display (integral cube 0 1 0.01))

(define (even? x)
  (= (remainder x 2) 0))

(define (simpson f a b n)
  (define h (/ (- b a) n))
  (define (new-f n1)
    (cond ((or (= n1 0) (= n1 n)) (f (+ a (* n1 h))))
          ((even? n1) (* 2 (f (+ a (* n1 h)))))
          (else (* 4 (f (+ a (* n1 h)))))))
  (define (inc n) (+ n 1)) 
  (* (/ h 3) (sum new-f 0 inc n)))

(newline)
(display (simpson cube 0 1 100))