Input
x^3 – 3 x
Polynomial discriminant
Delta = 108
Derivative
d/dx(x^3 – 3 x) = 3 (x^2 – 1)
Indefinite integral
integral (-3 x + x^3) dx = x^4/4 – (3 x^2)/2 + constant
Local maximum
max{x^3 – 3 x} = 2 at x = -1
Local minimum
min{x^3 – 3 x} = -2 at x = 1
Definite integral area below the axis between the smallest and largest real roots
integral_(-sqrt(3))^(sqrt(3)) (-3 x + x^3) theta(3 x – x^3) dx = -9/4 = -2.25
Definite integral area above the axis between the smallest and largest real roots
integral_(-sqrt(3))^(sqrt(3)) (-3 x + x^3) theta(-3 x + x^3) dx = 9/4 = 2.25