i.1.54 Double integrals
condition: Calculate \[ \iint_{G} y d x d y, \text { where } G=\{(x, y): 0 \leq y \leq x+1 \leq 2\} \text {. } \]
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.