i.1.63 Double integrals
condition: Change the order of integration: \[ \int_{0}^{1} d y \int_{0}^{y} f d x+\int_{1}^{\sqrt{2}} d y \int_{0}^{\sqrt{2-y^{2}}} f d x . \]
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.