so I am given

$\displaystyle \int_{0}^{2}\int_{-3\sqrt{4-x^2}/2}^{3\sqrt{4-x^2}/2} \Bigg(\frac{5}{\sqrt{2+x}} + y^3} \Bigg)dydx$

Could I do this as

$\displaystyle 2\int_{0}^{2}\int_{0}^{3\sqrt{4-x^2}/2} \Bigg(\frac{5}{\sqrt{2+x}} + y^3} \Bigg)dydx$

I remember doing some integrals in calculus 2 where you could do that. I think they were stuff dealing with the polar coordinates though