| Input |
|---|
| x^2 – 2 |
| Geometric figure |
| parabola |
| Alternate form |
| -(sqrt(2) – x) (x + sqrt(2)) |
| Polynomial discriminant |
| Delta = 8 |
| Derivative |
| d/dx(x^2 – 2) = 2 x |
| Indefinite integral |
| integral (-2 + x^2) dx = x^3/3 – 2 x + constant |
| Global minimum |
| min{x^2 – 2} = -2 at x = 0 |
| Definite integral |
| integral_(-sqrt(2))^(sqrt(2)) (-2 + x^2) dx = -(8 sqrt(2))/3~~-3.77124 |
| Definite integral area below the axis between the smallest and largest real roots |
| integral_(-sqrt(2))^(sqrt(2)) (-2 + x^2) theta(2 – x^2) dx = -(8 sqrt(2))/3~~-3.77124 |