Input
x^2 – 3 x – 18
Geometric figure
parabola
Polynomial discriminant
Delta = 81
Derivative
d/dx(x^2 – 3 x – 18) = 2 x – 3
Indefinite integral
integral (-18 – 3 x + x^2) dx = x^3/3 – (3 x^2)/2 – 18 x + constant
Global minimum
min{x^2 – 3 x – 18} = -81/4 at x = 3/2
Definite integral
integral_(-3)^6 (-18 – 3 x + x^2) dx = -243/2 = -121.5
Definite integral area below the axis between the smallest and largest real roots
integral_(-3)^6 (-18 – 3 x + x^2) theta(18 + 3 x – x^2) dx = -243/2 = -121.5