A calculus problem by Hummus a

Calculus Level 4

\[ \large\left(\displaystyle\lim _{ n\rightarrow \infty }{ \displaystyle\int _{ 0 }^{ \pi /2 }{ \sqrt [ n ]{ \sin ^{ n }{ x } +\cos ^{ n }{ x } } }\, dx }\right )^{ 2 } =\, ? \]

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