i.1.67 Double integrals
condition: Calculate the double integral over the area \( D \) : \[ \iint_{D} \frac{d x d y}{\sqrt{1-x^{2}-y^{2}}} ; \quad D: 0 \leq x^{2}+y^{2} \leq 1 ; x \leq y \text {. } \]
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.