X^2-10x

X^2-10x

Input
x^2 – 10 x
Geometric figure
parabola
Polynomial discriminant
Delta = 100
Derivative
d/dx(x^2 – 10 x) = 2 (x – 5)
Indefinite integral
integral (-10 x + x^2) dx = x^3/3 – 5 x^2 + constant
Global minimum
min{x^2 – 10 x} = -25 at x = 5
Definite integral
integral_0^10 (-10 x + x^2) dx = -500/3~~-166.667
Definite integral area below the axis between the smallest and largest real roots
integral_0^10 (-10 x + x^2) theta(10 x – x^2) dx = -500/3~~-166.667

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