Data update

Task/Numerical-integration/Julia/numerical-integration-2.jl

@@ -0,0 +1,24 @@
+leftrect(f, x, _) = f(x)
+midrect(f, x, h) = f(x + h / 2)
+rightrect(f, x, h) = f(x + h)
+trapezium(f, x, h) = (f(x) + f(x + h)) / 2
+simpson(f, x, h) = (f(x) + 4 * f(x + h / 2) + f(x + h)) / 6
+cube(x) = x * x * x
+reciprocal(x) = inv(x)
+
+function integrate(f, a, b, steps, meth)
+    h = (b - a) / steps
+    return h * sum(meth(f, a + i * h, h) for i in 0:steps-1)
+end
+
+for (a, b, steps, fun) in [
+    (0, 1, 100, cube),
+    (1, 100, 1000, reciprocal),
+    (0, 5000, 5_000_000, identity),
+    (0, 6000, 6_000_000, identity)]
+    for rule in [leftrect, midrect, rightrect, trapezium, simpson]
+        println(string(fun) * " integrated using " * string(rule))
+        println("    from $a to $b ($steps steps) = ",
+            round(integrate(fun, a, b, steps, rule), sigdigits=14))
+    end
+end