i.1.55 Double integrals
Condition: Change the order of integration and calculate the integral in the most rational way. \[ \int_{-1}^{1} d x \int_{-\sqrt{1-x^{2}}}^{1-x^{2}} y d y \]
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.