June 2018 Update

Task/Numerical-integration/Julia/numerical-integration.julia

@@ -1,8 +1,16 @@
-function simpson(f, a,b, n)
-    h = (b-a)/n
-    s = f(a + h/2)
+function simpson(f::Function, a::Number, b::Number, n::Integer)
+    h = (b - a) / n
+    s = f(a + h / 2)
     for i in 1:(n-1)
-        s += f(a + h*i + h/2) + 0.5 * f(a + h*i)
+        s += f(a + h * i + h / 2) + f(a + h * i) / 2
     end
-    h/6 * (f(a) + f(b) + 4*s)
+    return h/6 * (f(a) + f(b) + 4*s)
 end
+
+rst =
+    simpson(x -> x ^ 3, 0, 1, 100),
+    simpson(x -> 1 / x, 1, 100, 1000),
+    simpson(x -> x, 0, 5000, 5_000_000),
+    simpson(x -> x, 0, 6000, 6_000_000)
+
+@show rst