Input
x^2 – 25
Geometric figure
parabola
Alternate form
(x – 5) (x + 5)
Polynomial discriminant
Delta = 100
Derivative
d/dx(x^2 – 25) = 2 x
Indefinite integral
integral (-25 + x^2) dx = x^3/3 – 25 x + constant
Global minimum
min{x^2 – 25} = -25 at x = 0
Definite integral
integral_(-5)^5 (-25 + x^2) dx = -500/3~~-166.667
Definite integral area below the axis between the smallest and largest real roots
integral_(-5)^5 (-25 + x^2) theta(25 – x^2) dx = -500/3~~-166.667