i.1.69 Double integrals
condition: Calculate the double integral: \[ \iint_{D}\left(9 x^{2} y^{2}+25 x^{4} y^{4}\right) d x d y \] \[ D: x=1, y=x^{3}, y=-x^{\frac{1}{3}} \]
Double and iterated integrals over various areas of integration, conversion from Cartesian to polar coordinates, calculation of the Jacobian, changing the limits of integration, transformation of variables in the integral.