diff --git a/src/klausurvorbereitung/integration_simpson.py b/src/klausurvorbereitung/integration_simpson.py new file mode 100644 index 0000000..c993fe3 --- /dev/null +++ b/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 +""" diff --git a/src/klausurvorbereitung/integration_trapez.py b/src/klausurvorbereitung/integration_trapez.py index cc8a00b..2276e53 100644 --- a/src/klausurvorbereitung/integration_trapez.py +++ b/src/klausurvorbereitung/integration_trapez.py @@ -1,4 +1,6 @@ """ +Trapez-Regel + Integration der funktion: 2 I = | (x + sin(x))^(2/3)) dx