i.1.43 Double integrals
Condition: Calculate the double integral \( \iint_{D} f(x ; y) d x d y \) over the region \( D \) with the given boundary \( \partial D \). \[ f(x ; y)=y-2 x, \quad \partial D:\left\{\begin{array}{c} y=x^{2}, x+y=2 \\ y=0 \end{array}\right\} . \]
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.