The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6, 7 is ______.

$\text{Digits allowed: } 0, 2, 3, 4, 6, 7$

$\text{Range: } 2022 \le N \le 4482$

$\text{To find: number of 4-digit numbers } N$

$N \text{ is 4-digit} \Rightarrow \text{first digit } \neq 0$

$N \le 4482 \Rightarrow \text{first digit} \in \{2, 3, 4\}$

$\text{Plan: split by the first digit}$

$\text{First digit} \in \{2, 3, 4\}$

Case d₁ = 3: 3abc 3000 ≤ 3abc ≤ 3777

$\text{count} = 6^3 = 216$

Case d₁ = 2: 2abc ≥ 2022 ⇒ abc ≥ 022 All 2abc = 6³ = 216 Exclude 2abc < 2022 ⇔ abc < 022

$2000\text{ to }2007: 6 \text{ values}$

$2020: 1 \text{ value}$

$\text{total excluded} = 7$

$d_1 = 2:\ 216 - 7 = 209$

Case d₁ = 4: 4abc ≤ 4482 ⇒ abc ≤ 482

$a \in \{0, 2, 3\}:\ 3 \times 6^2 = 108$

$a = 4:\ 44bc \le 4482 \text{ always} \Rightarrow 6^2 = 36$

$d_1 = 4:\ 108 + 36 = 144$

$209 + 216 + 144 = 569$

$3 \times 216 = 648$

$648 - 7 - 72 = 569$

$(7 < 2022,\ 72 > 4482)$

$\boxed{569}$