Input
x^2 + 5 x + 4
Geometric figure
parabola
Polynomial discriminant
Delta = 9
Derivative
d/dx(x^2 + 5 x + 4) = 2 x + 5
Indefinite integral
integral (4 + 5 x + x^2) dx = x^3/3 + (5 x^2)/2 + 4 x + constant
Global minimum
min{x^2 + 5 x + 4} = -9/4 at x = -5/2
Definite integral
integral_(-4)^(-1) (4 + 5 x + x^2) dx = -9/2 = -4.5
Definite integral area below the axis between the smallest and largest real roots
integral_(-4)^(-1) (4 + 5 x + x^2) theta(-4 – 5 x – x^2) dx = -9/2 = -4.5