i.1.77 Double integrals
condition: Change the order of integration. \[ \int_{-2}^{-1} d y \int_{-\sqrt{2+y}}^{0} f(x, y) d x+\int_{-1}^{0} d y \int_{-\sqrt{y}}^{0} f(x, y) d x \]
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.