4x^2+4x

4x^2+4x

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

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