exericse 1.29

gistfile1.lisp

(defun sum (term a next b)
  (if (> a b)
      0
    (+ (funcall term a)
       (sum term (funcall next a) next b))))
(defun cube (x) (* x x x))
(defun integral (f a b dx)
  (defun add-dx (x) (+ x dx))
  (* (sum f
          (+ a (/ dx 2.0))
          #'add-dx
          b)
     dx))
(integral #'cube 0 1 0.01)

(defun simp-integral (f a b n)
  (let ((h (/ (- b a) n)))
    (defun add-dx (x) (+ x (* 2 h)))
    (defun simp-term (a)
      (+ (funcall f a)
         (* 4 (funcall f (+ a h)))
         (funcall f (+ a (* 2 h)))))
    (* (/ h 3.0)
       (sum #'simp-term a #'add-dx (- b (* 2 h))))
    ))

(simp-integral #'cube 0 1 100)