1.
d(x) = f(x) - g(x) = x^3 - (x^2 + 2·x) = x^3 - x^2 - 2·x
Schnittstellen d(x) = 0
x^3 - x^2 - 2·x = x·(x^2 - x - 2) = x·(x + 1)·(x - 2) = 0
x = 2 ∨ x = -1 ∨ x = 0
∫ (-1 bis 0) (x^3 - x^2 - 2·x) dx = 5/12
∫ (0 bis 2) (x^3 - x^2 - 2·x) dx = - 8/3
A = 5/12 + 8/3 = 37/12