| Input |
|---|
| x^2 – 25 |
| Geometric figure |
| parabola |
| Alternate form |
| (x – 5) (x + 5) |
| Polynomial discriminant |
| Delta = 100 |
| Derivative |
| d/dx(x^2 – 25) = 2 x |
| Indefinite integral |
| integral (-25 + x^2) dx = x^3/3 – 25 x + constant |
| Global minimum |
| min{x^2 – 25} = -25 at x = 0 |
| Definite integral |
| integral_(-5)^5 (-25 + x^2) dx = -500/3~~-166.667 |
| Definite integral area below the axis between the smallest and largest real roots |
| integral_(-5)^5 (-25 + x^2) theta(25 – x^2) dx = -500/3~~-166.667 |