9.1.23 Double integrals

Problem: Find the double integral over the area \( D \), bounded by the indicated lines: \[ \begin{array}{l} \iint_{D}\left(24 x y+18 x^{2} y^{2}\right) d x d y, \\ D: x=1, \quad y=x^{3}, \quad y=-\sqrt[3]{x} . \end{array} \]