9.1.18 Double integrals

Problem: Find the double integral over the given area \( S \) : \[ I=\iint_{(S)} \sqrt{a^{2}-x^{2}-y^{2}}, \] \( S:\left(x^{2}+y^{2}\right)^{2}=a^{2}\left(x^{2}-y^{2}\right), \quad x \geq 0 \).