Input
x^2 + x – 20
Geometric figure
parabola
Polynomial discriminant
Delta = 81
Derivative
d/dx(x^2 + x – 20) = 2 x + 1
Indefinite integral
integral (-20 + x + x^2) dx = x^3/3 + x^2/2 – 20 x + constant
Global minimum
min{x^2 + x – 20} = -81/4 at x = -1/2
Definite integral
integral_(-5)^4 (-20 + x + x^2) dx = -243/2 = -121.5
Definite integral area below the axis between the smallest and largest real roots
integral_(-5)^4 (-20 + x + x^2) theta(20 – x – x^2) dx = -243/2 = -121.5