i.1.53 Double integrals
condition: Go to polar coordinates and write the integral \( \iint_{G} f\left(\sqrt{x^{2}+y^{2}}\right) d x d y \) in repeated form, where \[ G=\left\{(x, y): x^{2}+y^{2}+y^{2}+10 y \leq 0, y \geq \sqrt{3} x\right\} \]
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.