probability - Calculate the expected value

To get the expected value of $E(X), E(Y)$ and $E(X, Y)$ given:

$$f_{X,Y}(x,y) = 3x$$
where $0\le x \le y \le 1.$

My solution is, first get the margin distribution:

$$\begin{aligned} f_x(x) &= 3x(1-x) \\ f_y(y) &= \frac{3}{2} y^2 \end{aligned}$$

Then calculate the expected value:

$$\begin{aligned} E(X) &= \int_0^y 3x^2(1-x) \; dx = y^3-\frac{3}{4} y^4 \\ E(Y) &= \int_x^1 \frac{3}{2} y^3 \; dy = \frac{3}{8} (1 - x^4) \end{aligned}$$

and

$$\begin{aligned} E(XY)=\int_0^y \int_x^1 xy \cdot 3x \;dy\; dx = \frac{1}{2} y^3 - \frac{3}{10} y^5 \end{aligned}$$

However, my calculated expected values contain variable $x$ and $y$, do I make some mistakes?

Answer

[after you added the joint distribution of $X,Y$]:
to find $\mathbf{E}XY$ use

$$\int_{0}^{1} \int_{0}^{y}xy f(x,y)dx dy$$
Can you handle the rest?