4x-x^2
| Input |
|---|
| 4 x – x^2 |
| Geometric figure |
| parabola |
| Polynomial discriminant |
| Delta = 16 |
| Derivative |
| d/dx(4 x – x^2) = 4 – 2 x |
| Indefinite integral |
| integral (4 x – x^2) dx = 2 x^2 – x^3/3 + constant |
| Global maximum |
| max{4 x – x^2} = 4 at x = 2 |
| Definite integral |
| integral_0^4 (4 x – x^2) dx = 32/3~~10.6667 |
| Definite integral area above the axis between the smallest and largest real roots |
| integral_0^4 (4 x – x^2) theta(4 x – x^2) dx = 32/3~~10.6667 |