1 665c255d 2023-08-04 jrmu (defun cube (x)
 2 665c255d 2023-08-04 jrmu   (* x x x))
 3 665c255d 2023-08-04 jrmu (defun sum (term a next b)
 4 665c255d 2023-08-04 jrmu   (if (> a b)
 5 665c255d 2023-08-04 jrmu       0
 6 665c255d 2023-08-04 jrmu     (+ (funcall term a)
 7 665c255d 2023-08-04 jrmu        (sum term (funcall next a) next b))))
 8 665c255d 2023-08-04 jrmu (defun sum-integers (a b)
 9 665c255d 2023-08-04 jrmu   (sum #'identity a #'1+ b))
10 665c255d 2023-08-04 jrmu (defun pi-sum (a b)
11 665c255d 2023-08-04 jrmu   (defun pi-term (x)
12 665c255d 2023-08-04 jrmu     (/ 1.0 (* x (+ x 2))))
13 665c255d 2023-08-04 jrmu   (defun pi-next (x)
14 665c255d 2023-08-04 jrmu     (+ x 4))
15 665c255d 2023-08-04 jrmu   (sum #'pi-term a #'pi-next b))
16 665c255d 2023-08-04 jrmu (defun integral (f a b dx)
17 665c255d 2023-08-04 jrmu   (defun add-dx (x)
18 665c255d 2023-08-04 jrmu     (+ x dx))
19 665c255d 2023-08-04 jrmu   (* (sum f (+ a (/ dx 2.0)) #'add-dx b) dx))
20 665c255d 2023-08-04 jrmu 
21 665c255d 2023-08-04 jrmu (defun simpson-integral (f a b n)
22 665c255d 2023-08-04 jrmu   (let ((h (float (/ (- b a) n))))
23 665c255d 2023-08-04 jrmu     (defun simpson-term (k)
24 665c255d 2023-08-04 jrmu       (* (funcall f (+ a (* k h)))
25 665c255d 2023-08-04 jrmu 	 (cond ((or (= k 0) (= k n)) 1)
26 665c255d 2023-08-04 jrmu 	       ((oddp k) 4)
27 665c255d 2023-08-04 jrmu 	       (t 2))))
28 665c255d 2023-08-04 jrmu     (* (/ h 3)
29 665c255d 2023-08-04 jrmu        (sum #'simpson-term 0 #'1+ n))))