X^2-4x+2

X^2-4x+2

Input
x^2 – 4 x + 2
Geometric figure
parabola
Polynomial discriminant
Delta = 8
Derivative
d/dx(x^2 – 4 x + 2) = 2 (x – 2)
Indefinite integral
integral (2 – 4 x + x^2) dx = x^3/3 – 2 x^2 + 2 x + constant
Global minimum
min{x^2 – 4 x + 2} = -2 at x = 2
Definite integral
integral_(2 – sqrt(2))^(2 + sqrt(2)) (2 – 4 x + x^2) dx = -(8 sqrt(2))/3~~-3.77124
Definite integral area below the axis between the smallest and largest real roots
integral_(2 – sqrt(2))^(2 + sqrt(2)) (2 – 4 x + x^2) theta(-2 + 4 x – x^2) dx = -(8 sqrt(2))/3~~-3.77124

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