i.1.56 Double integrals
Condition: Present the double integral \( \iint_{G} f(x, y) d x d y \) in the form of a repeated integral: a) with outer integration over \( x \), b) with outer integration over \( y \), if the region \( D \) is specified by the specified restrictions: \[ D: y \leq \sqrt{4-x^{2}}, \quad y \geq x, \quad x \geq 0 \]
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.