i.1.47 Double integrals
Condition: Draw the region to which the double integral is extended, change the order of integration and write the integral in the polar coordinate system. \[ \int_{-2}^{-1} d y \int_{-(2+y)}^{0} f(x, y) d x+\int_{-1}^{0} d y \int_{\sqrt[3]{y}}^{0} f(x, y) d x \]
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.