in-class/15-review-simpsons-rule.scm

in-class/15-review-simpsons-rule.scm

@@ -0,0 +1,67 @@
+(define (sum-integers a b)
+  (if (> a b)
+      0
+      (+ a (sum-integers (+ a 1) b))))
+
+(sum-integers 2 5)
+
+(if #f 'f
+    (+ 2 
+       ;(sum-integers 3 5)
+       (if #f 'f
+           (+ 3
+              ;(sum-int 4 5)
+              (if #f 'f
+                  (+ 4
+                     ;(sum-int 5 5)
+                     5
+                     0))))))
+
+(define (sum-cubes a b)
+  (if (> a b)
+      0
+      (+ (cube a) (sum-cubes (+ a 1) b))))
+
+(define (sum f a dx b)
+  (if (> a b)
+      0
+      (+ (f a) (sum f (dx a) dx b))))
+
+;; Exercise 1.29
+
+(define (cube x) (* x x x))
+
+(define (integral f a b dx)
+  (define (add-dx x) (+ x dx))
+  (* (sum f (+ a (/ dx 2.0)) add-dx b)
+     dx))
+
+(define (simpsons-rule f a b n) 
+  (define (poop start n) 
+    (if (= n 0)
+        (f a)
+        (+ (* 
+            (f (+ a (/ (- b a) n)))
+            (cond 
+              ((= n start) 1)
+              ((even? n) 2) 
+              (else 4)))
+           (poop start (- n 1))))) 
+  (* (/ (/ (- b a) n) 3.0)
+     (poop n n)))
+
+(define (simpsons-rule f a b n)
+  (define (h n)
+    (/ (- b a) n))
+  (define (loop n)
+    (if (= n 0)
+        (f a)
+        (+ (* (if (even? n) 2 4)
+              (h n))
+           (loop (- n 1)))))
+  (* (/ (h n) 3.0)
+     (+ (h n) (loop (- n 1)))))
+
+(integral cube 2 10 4)
+
+(simpsons-rule cube 2 10 4)