y = -x^(3/2)/sqrt(2)
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y = x^(3/2)/sqrt(2)
Polynomial discriminant:
Δ_x = -108 y^4
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Integer roots:
x = 2, y = ± 2
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x = 8, y = ± 16
x = 18, y = ± 54
x = 0, y = 0
Properties as a function:Domain:
R^2
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Range:
R (all real numbers)
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Partial derivatives:Step-by-step solution
d/(dx)(2 y^2 - x^3) = -3 x^2
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d/(dy)(2 y^2 - x^3) = 4 y
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Indefinite integral:Step-by-step solution
integral(-x^3 + 2 y^2) dx = 2 x y^2 - x^4/4 + constant
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Definite integral over a disk of radius R:
integral integral_(x^2 + y^2
Definite integral over a square of edge length 2 L:
integral_(-L)^L integral_(-L)^L (-x^3 + 2 y^2) dy dx = (8 L^4)/3
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