5y(2y-3)+(2y-3)

5y(2y-3)+(2y-3)

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

Leave a Reply

Your email address will not be published. Required fields are marked *