i.1.74 Double integrals
condition: Going to polar coordinates, calculate the double integral: \[ \begin{array}{l} \iint_{D} \sqrt{\frac{1-x^{2}-y^{2}}{1+x^{2}+y^{2}}} d x d y \\ D: x^{2}+y^{2} \leq 1, \quad x \geq 0, \quad y \geq 0 \end{array} \]
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.