i.1.49 Double integrals
Condition: Given the double integral \( \iint_{D} f(x, y) d x d y \) over the domain \( D \). a) write it down as a repeated integral in Cartesian coordinates, b) change the order of integration, c) go to polar coordinates. \[ \left\{\begin{array}{c} 0 \leq y \leq 3 \\ \sqrt{6 y-y^{2}} \leq x \leq 3 \end{array}\right. \]
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.