Input
x^2 – 3 x
Geometric figure
parabola
Polynomial discriminant
Delta = 9
Derivative
d/dx(x^2 – 3 x) = 2 x – 3
Indefinite integral
integral (-3 x + x^2) dx = x^3/3 – (3 x^2)/2 + constant
Global minimum
min{x^2 – 3 x} = -9/4 at x = 3/2
Definite integral
integral_0^3 (-3 x + x^2) dx = -9/2 = -4.5
Definite integral area below the axis between the smallest and largest real roots
integral_0^3 (-3 x + x^2) theta(3 x – x^2) dx = -9/2 = -4.5