A calculus problem by Hobart Pao

Calculus Level 4

\[\large \mathscr{I} = \displaystyle \int \limits_{0}^{\infty} \int \limits_{0}^{\infty} \dfrac{\sin x \sin y}{xy} \, dy \, dx \]

Find \( \left \lfloor 1000\mathscr{I} \right \rfloor \)

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