Input
x^2 + 2 x – 24
Geometric figure
parabola
Polynomial discriminant
Delta = 100
Derivative
d/dx(x^2 + 2 x – 24) = 2 (x + 1)
Indefinite integral
integral (-24 + 2 x + x^2) dx = x^3/3 + x^2 – 24 x + constant
Global minimum
min{x^2 + 2 x – 24} = -25 at x = -1
Definite integral
integral_(-6)^4 (-24 + 2 x + x^2) dx = -500/3~~-166.667
Definite integral area below the axis between the smallest and largest real roots
integral_(-6)^4 (-24 + 2 x + x^2) theta(24 – 2 x – x^2) dx = -500/3~~-166.667