16x^4-81

16x^4-81

Input
16 x^4 – 81
Alternate form
(2 x – 3) (2 x + 3) (4 x^2 + 9)
Polynomial discriminant
Delta = -557256278016
Derivative
d/dx(16 x^4 – 81) = 64 x^3
Indefinite integral
integral (-81 + 16 x^4) dx = (16 x^5)/5 – 81 x + constant
Global minimum
min{16 x^4 – 81} = -81 at x = 0
Definite integral
integral_(-3/2)^(3/2) (-81 + 16 x^4) dx = -972/5 = -194.4
Definite integral area below the axis between the smallest and largest real roots
integral_(-3/2)^(3/2) (-81 + 16 x^4) theta(81 – 16 x^4) dx = -972/5 = -194.4

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