9.1.2 Double integrals

Problem: Calculate the values of double integrals: 1) \( \iint_{(D)}\left(8 x y+18 x^{2} y^{2}\right) d x d y, \quad D:\left\{\begin{array}{c}x=1 \\ y=\sqrt[3]{x} \\ y=-x^{2}, \quad(x \geq 0)\end{array}\right. \) 2) \( \iint 4 y^{2} \sin 2 x y d x d y, D:\left\{\begin{array}{c}x=0 \\ y=\sqrt{2 \pi} \\ y=2 x\end{array}\right. \)