3x^2-1

3x^2-1

Input
3 x^2 – 1
Geometric figure
parabola
Alternate form
-1/3 (sqrt(3) – 3 x) (3 x + sqrt(3))
Polynomial discriminant
Delta = 12
Derivative
d/dx(3 x^2 – 1) = 6 x
Indefinite integral
integral (-1 + 3 x^2) dx = x^3 – x + constant
Global minimum
min{3 x^2 – 1} = -1 at x = 0
Definite integral
integral_(-1/sqrt(3))^(1/sqrt(3)) (-1 + 3 x^2) dx = -4/(3 sqrt(3))~~-0.7698
Definite integral area below the axis between the smallest and largest real roots
integral_(-1/sqrt(3))^(1/sqrt(3)) (-1 + 3 x^2) theta(1 – 3 x^2) dx = -4/(3 sqrt(3))~~-0.7698

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