Independence of RV

A certain joint probability density function is given by the formula

fXY(xy)=π2xsin(xy),f_{XY} (xy) = \dfrac{\sqrt{\pi}}{2} x\sin (xy),

where xx and yy are drawn from the rectangle [0,π]×[0,π].\big[0,\sqrt{\pi}\big]\times \big[0,\sqrt{\pi}\big].

Are the random variables XX and YY independent?

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