| 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 |
