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 |