Input
x^2 – 3 x – 40
Geometric figure
parabola
Polynomial discriminant
Delta = 169
Derivative
d/dx(x^2 – 3 x – 40) = 2 x – 3
Indefinite integral
integral (-40 – 3 x + x^2) dx = x^3/3 – (3 x^2)/2 – 40 x + constant
Global minimum
min{x^2 – 3 x – 40} = -169/4 at x = 3/2
Definite integral
integral_(-5)^8 (-40 – 3 x + x^2) dx = -2197/6~~-366.167
Definite integral area below the axis between the smallest and largest real roots
integral_(-5)^8 (-40 – 3 x + x^2) theta(40 + 3 x – x^2) dx = -2197/6~~-366.167