List of top Statistics Questions on Double and triple integrals

Let \[ I = \pi^2 \int_0^1 \int_0^1 y^2 \cos \pi(1 + xy) \, dx \, dy. \] The value of \( I \) is equal to _________ (answer in integer).

Let \[ I = \pi^2 \int_0^1 \int_0^1 y^2 \cos \pi(1 + xy) \, dx \, dy. \] The value of \( I \) is equal to _________ (answer in integer).