i.1.57 Double integrals
condition: Calculate the double integral using polar coordinates: \[ \int_{-\sqrt{5}}^{\sqrt{5}} d x \int_{-\sqrt{5-x^{2}}}^{0} \frac{d y}{\sqrt{2+x^{2}+y^{2}}} \]
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.