1. Among the integers $1,2, \cdots, 2011$, the number of integers that can be expressed in the form $[x[x]]$ is $\qquad$, where $[x]$ denotes the greatest integer not exceeding the real number $x$.
2. 1.990.
Let $x=k+a, k=[x], 0 \leqslant a<1$. Then $[x[x]]=[k(k+a)]=k^{2}+[k a]$.
Therefore, $k^{2}, k^{2}+1, \cdots, k^{2}+k-1(k=1,2$, $\cdots, 44)$ can all be expressed in the form of $[x[x]]$. Hence, the number of integers that meet the requirement is
$$
1+2+\cdots+44=990 \text { (numbers). }
$$