Covariance/correlation coefficient - Where did I go wrong?

Problem

Let X and Y be two random variables with the following joint pdf:
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$f_{X,Y}(x,y) = 2$ for $x+y<1, x>0, y>0.$

$f_{X,Y}(x,y) = 0, otherwise.$

a) Find the marginal densities of X and Y .

b) Calculate Cov(X, Y) and the correlation coefficient ρ(X, Y).

Attempt

a)

$f_{x}(x) = int_0^{1-x}2 dy = 2(1-x) = -2x+2$

$f_{y}(y) = int_0^{1-y}2 dx = 2(1-y) = -2y+2$

b) i) covariance

$Cov(X, Y) = E(XY) – E(X)E(Y) = $

$intint xy ⋅ f(x,y) dy dx – int x ⋅ f(x) dx ⋅ int y ⋅ f(y) dy = $

$int_0^1int_0^{1-x} (2xy) dy dx – int_0^1 (-2x^2 + 2x) dx ⋅ int_0^1 (-2y^2 + 2y) dy $

$int_0^1int_0^{1-x} (2xy) dy dx = int_0^1 frac{2x(1-x)}{2} dx = int_0^1 x – x^2 dx = frac{2}{3} $

$int_0^1 (-2x^2 + 2x) dx = int_0^1 (-2y^2 + 2y) dy = frac{-2}{3} + 1 = frac{1}{3} $

$frac{2}{3} – frac{1}{3} ⋅ frac{1}{3} = frac{5}{9} = Cov(X, Y)$

ii) correlation coefficient

$ρ(X, Y) = frac{Cov(X, Y)}{SD_x⋅SD_y}$

$SD_x = sqrt{Var(X)}$

$SD_y = sqrt{Var(Y)}$

$E(X^2) = E(Y^2) = frac{1}{6}$

$E(X) = E(Y) = frac{1}{3}$ (from part b.i.)

$Var(X) = Var(Y) = E(X^2) – (E(X))^2 = frac{1}{6} – frac{1}{9} = frac{1}{18} $

$ρ(X, Y) = frac{Cov(X, Y)}{SD_x⋅SD_y} = frac{5/9}{1/18} = 10$

I know the correlation coefficient cannot be 10, but where did I go wrong?