\[\iint4(x^{4}-y^{4})\sin(2xy) \, dx \; dy \]

Calculate the integral above over the region bounded by the following 4 curves

\[\begin{cases} x^{2}-y^{2}=1 \\ x^{2}-y^{2}=2 \\ 2xy = \dfrac \pi 2 \\ 2xy = \pi \end{cases} \]

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