Data commit

Task/Numerical-integration/Racket/numerical-integration-1.rkt

@@ -0,0 +1,23 @@
+#lang racket
+(define (integrate f a b steps meth)
+  (define h (/ (- b a) steps))
+  (* h (for/sum ([i steps])
+         (meth f (+ a (* h i)) h))))
+
+(define (left-rect f x h) (f x))
+(define (mid-rect f x h)  (f (+ x (/ h 2))))
+(define (right-rect f x h)(f (+ x h)))
+(define (trapezium f x h) (/ (+ (f x) (f (+ x h))) 2))
+(define (simpson f x h)   (/ (+ (f x) (* 4 (f (+ x (/ h 2)))) (f (+ x h))) 6))
+
+(define (test f a b s n)
+  (displayln n)
+  (for ([meth (list left-rect mid-rect right-rect trapezium simpson)]
+        [name '(    left-rect mid-rect right-rect trapezium simpson)])
+    (displayln (~a name ":\t" (integrate f a b s meth))))
+  (newline))
+
+(test (λ(x) (* x x x)) 0.    1.     100 "CUBED")
+(test (λ(x) (/ x))     1.  100.    1000 "RECIPROCAL")
+(test (λ(x) x)         0. 5000. 5000000 "IDENTITY")
+(test (λ(x) x)         0. 6000. 6000000 "IDENTITY")

Task/Numerical-integration/Racket/numerical-integration-2.rkt

@@ -0,0 +1,27 @@
+CUBED
+left-rect:	0.24502500000000005
+mid-rect:	0.24998750000000006
+right-rect:	0.25502500000000006
+trapezium:	0.250025
+simpson:	0.25
+
+RECIPROCAL
+left-rect:	4.65499105751468
+mid-rect:	4.604762548678376
+right-rect:	4.55698105751468
+trapezium:	4.605986057514676
+simpson:	4.605170384957133
+
+IDENTITY
+left-rect:	12499997.5
+mid-rect:	12500000.0
+right-rect:	12500002.5
+trapezium:	12500000.0
+simpson:	12500000.0
+
+IDENTITY
+left-rect:	17999997.000000004
+mid-rect:	17999999.999999993
+right-rect:	18000003.000000004
+trapezium:	17999999.999999993
+simpson:	17999999.999999993