9.1.10 Double integrals

Problem: Calculate the double integral of the function \( x y \) over the area \( G \), given by the crossing of lines given parametrically: \[ G:\left\{\begin{array}{l} x=a \cos ^{3} t \\ y=a \sin ^{3} t \\ x=0, y=0 \end{array}\left(0 \leq t \leq \frac{\pi}{2}\right) \quad \iint_{G} x y d x d y-?\right. \]