4x^2-1

4x^2-1

Input
4 x^2 – 1
Geometric figure
parabola
Alternate form
(2 x – 1) (2 x + 1)
Polynomial discriminant
Delta = 16
Derivative
d/dx(4 x^2 – 1) = 8 x
Indefinite integral
integral (-1 + 4 x^2) dx = (4 x^3)/3 – x + constant
Global minimum
min{4 x^2 – 1} = -1 at x = 0
Definite integral
integral_(-1/2)^(1/2) (-1 + 4 x^2) dx = -2/3~~-0.666667
Definite integral area below the axis between the smallest and largest real roots
integral_(-1/2)^(1/2) (-1 + 4 x^2) theta(1 – 4 x^2) dx = -2/3~~-0.666667

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