Simpson-Regel. Trapez Regel Beschreibung hinzugefügt

src/klausurvorbereitung/integration_simpson.py

@@ -0,0 +1,45 @@
+"""
+Simpson-Regel
+
+Integration der funktion:
+    2
+I = | (x + sin(x))^(2/3)) dx
+    0
+"""
+
+import numpy as np
+import scipy.integrate as ig
+
+# Parameter
+x_0 = 0
+x_E = 2
+n = 10
+N = 201
+pr = 6
+
+f = lambda x: np.sqrt(x + np.sin(x))
+
+# Berechnung
+for k in range(0, n):
+    x_data = np.linspace(x_0, x_E, N)
+    y_data = f(x_data)
+    I = ig.simpson(y=y_data, x=x_data)
+    print(f"I = {I:#.16g} | N = {N:g}")
+    N *= 2
+print(f"I = {I:#.{pr}g}")
+
+"""
+Ausgabe:
+
+I = 2.490070783046884 | N = 201
+I = 2.490260152603558 | N = 402
+I = 2.490326897146905 | N = 804
+I = 2.490350466364332 | N = 1608
+I = 2.490358796310514 | N = 3216
+I = 2.490361741357393 | N = 6432
+I = 2.490362782708113 | N = 12864
+I = 2.490363150933651 | N = 25728
+I = 2.490363281138151 | N = 51456
+I = 2.490363327177379 | N = 102912
+I = 2.49036
+"""

src/klausurvorbereitung/integration_trapez.py

@@ -1,4 +1,6 @@
 """
+Trapez-Regel
+
 Integration der funktion:
     2
 I = | (x + sin(x))^(2/3)) dx