적분 $\displaystyle \int _ {0} ^ {1} {\int _ {x} ^ {1} {x^ {2022} \sqrt {1+y^ {2024}}}} dy dx$ 의 값은?

• ①$\displaystyle \frac{1} {2024 \cdot 3036} \left (2 \sqrt 2 -1 \right)$
• ②$\displaystyle \frac{1} {2023 \cdot 3036} \left (2 \sqrt 2 -1 \right)$
• ③$\displaystyle \frac{1} {2024 \cdot 3036} \left (\sqrt 2 -1 \right)$
• ④$\displaystyle \frac{1} {2023 \cdot 3036} \left (\sqrt 2 -1 \right)$