List all the elements of the following set:
$C = \{ x : x \text{ is an integer; } x^2 \le 4 \}$

The set $C$ is defined as $C = \{ x : x \text{ is an integer; } x^2 \le 4 \}$.
We need to find all integers $x$ such that their square is less than or equal to $4$.
Testing integers:
$(-3)^2 = 9 > 4$
$(-2)^2 = 4 \le 4$
$(-1)^2 = 1 \le 4$
$0^2 = 0 \le 4$
$1^2 = 1 \le 4$
$2^2 = 4 \le 4$
$3^2 = 9 > 4$
Thus,the integers satisfying the condition are $\{-2, -1, 0, 1, 2\}$.
Therefore,$C = \{-2, -1, 0, 1, 2\}$.