| Input |
| 5 y (2 y – 3) + (2 y – 3) |
| Result |
| 5 (2 y – 3) y + 2 y – 3 |
| Geometric figure |
| parabola |
| Polynomial discriminant |
| Delta = 289 |
| Derivative |
| d/dy(5 y (2 y – 3) + (2 y – 3)) = 20 y – 13 |
| Indefinite integral |
| integral (-3 + 2 y + 5 y (-3 + 2 y)) dy = (10 y^3)/3 – (13 y^2)/2 – 3 y + constant |
| Global minimum |
| min{5 y (2 y – 3) + (2 y – 3)} = -289/40 at y = 13/20 |
| Definite integral |
| integral_(-1/5)^(3/2) (-3 + 2 y + 5 y (-3 + 2 y)) dy = -4913/600~~-8.18833 |
| Definite integral area below the axis between the smallest and largest real roots |
| integral_(-1/5)^(3/2) (-3 + 2 y + 5 y (-3 + 2 y)) theta(3 – 2 y – 5 y (-3 + 2 y)) dy = -4913/600~~-8.18833 |
