i.1.79 Double integrals
Condition: Calculate the value of the double integral over the area \(D\). \[ \iint_{(D)} y^{2} e^{-\frac{x y}{8}} d x d y ; \quad D: x=0 ; y=4 ; y=2 x . \]
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.