i.1.46 Double integrals
condition: Calculate the coordinates of the center of gravity of the homogeneous plane of the plate, bounded by the circle \( x^{2}+y^{2}=4 \) and the straight lines \( x=2 \) and \( y=2 \).
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.