Mean of the smaller coordinate under density c(1 minus y)

The pair $(X_1,X_2)$ has joint density $c(1-x_2)$ when $0\le x_1\le x_2\le1$ and $0$ otherwise, with $c$ chosen to make it a density. Find $\mathbb{E}[X_1]$.

$1/4$. Normalisation forces $c=6$ and the marginal of $X_2$ is $6x_2(1-x_2)$. Given $X_2$, $X_1$ is uniform on $[0,X_2]$, so $\mathbb{E}X_1=\tfrac12\mathbb{E}X_2=\tfrac12\cdot\tfrac12=\tfrac14$.