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