X^2+2x-1

X^2+2x-1

Input
x^2 + 2 x – 1
Geometric figure
parabola
Polynomial discriminant
Delta = 8
Derivative
d/dx(x^2 + 2 x – 1) = 2 (x + 1)
Indefinite integral
integral (-1 + 2 x + x^2) dx = x^3/3 + x^2 – x + constant
Global minimum
min{x^2 + 2 x – 1} = -2 at x = -1
Definite integral
integral_(-1 – sqrt(2))^(-1 + sqrt(2)) (-1 + 2 x + x^2) dx = -(8 sqrt(2))/3~~-3.77124
Definite integral area below the axis between the smallest and largest real roots
integral_(-1 – sqrt(2))^(-1 + sqrt(2)) (-1 + 2 x + x^2) theta(1 – 2 x – x^2) dx = -(8 sqrt(2))/3~~-3.77124

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