It looks like the starting integral is
[tex]\displaystyle \int_{-11}^{11} \int_0^{\sqrt{121-x^2}} dy\,dx[/tex]
The key is recognizing the domain of integration as the semicircle centered at the origin with radius 11. In polar coordinates, this integral transforms to
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{11} r \, dr \, d\theta}[/tex]
