Question

Berechne den Inhalt der Fläche zwischen den beiden Kurven:

f(x) = x²

g(x) = x + 6

 

Answer 1

d(x) = f(x) - g(x) = x^2 - (x + 6) = x^2 - x - 6
D(x) = 1/3*x^3 - 1/2*x^2 - 6x

d(x) = 0

x^2 - x - 6 = 0
x = -2
x = 3

D(3) - D(-2) = - 27/2 - (22/3) = - 125/6 = -20.83333333

Die Fläche beträgt also ca. 20.8 FE (Flächeneinheiten).