Input
x^4 – 13 x^2 + 36
Polynomial discriminant
Delta = 360000
Derivative
d/dx(x^4 – 13 x^2 + 36) = 4 x^3 – 26 x
Indefinite integral
integral (36 – 13 x^2 + x^4) dx = x^5/5 – (13 x^3)/3 + 36 x + constant
Local maximum
max{x^4 – 13 x^2 + 36} = 36 at x = 0
Definite integral area below the axis between the smallest and largest real roots
integral_(-3)^3 (36 – 13 x^2 + x^4) theta(-36 + 13 x^2 – x^4) dx = -124/15~~-8.26667
Definite integral area above the axis between the smallest and largest real roots
integral_(-3)^3 (36 – 13 x^2 + x^4) theta(36 – 13 x^2 + x^4) dx = 1312/15~~87.4667