i.1.45 Double integrals
condition: Construct a domain of integration and change the order of integration. \[ \int_{1}^{2} d x \int_{2-\frac{x^{2}}{2}}^{\frac{1}{2}(x+2)} f(x, y) d y \]
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.