i.1.52 Double integrals
condition: Change the order of integration: \[ \int_{0}^{1} d y \int_{0}^{\sqrt{y}} f d x+\int_{1}^{2} d y \int_{0}^{\sqrt{2-y}} f d x \]
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.