Question

Number of integral values of $x^2$ if $x\in (-3,2]$ is

Answer 1

Here $x\in (-3,2]$
Splitting into intervals
$x\in (-3,0)\cup [0,2]$
For $x\in (-3,0)$
$x^2\in (0,9)$
For $x\in [0,2]$
$\Rightarrow x^2\in [0,4]$
$\therefore x^2\in [0,9)$
So, number of integral values of $x^2$ is $9$