Input
x^2 – 2
Geometric figure
parabola
Alternate form
-(sqrt(2) – x) (x + sqrt(2))
Polynomial discriminant
Delta = 8
Derivative
d/dx(x^2 – 2) = 2 x
Indefinite integral
integral (-2 + x^2) dx = x^3/3 – 2 x + constant
Global minimum
min{x^2 – 2} = -2 at x = 0
Definite integral
integral_(-sqrt(2))^(sqrt(2)) (-2 + x^2) dx = -(8 sqrt(2))/3~~-3.77124
Definite integral area below the axis between the smallest and largest real roots
integral_(-sqrt(2))^(sqrt(2)) (-2 + x^2) theta(2 – x^2) dx = -(8 sqrt(2))/3~~-3.77124