# Convergence of improper double integral

Calculus Level 5

Inital conditions of the problem:

Let be $D := \{ (x,y)\in \mathbb{R}^2 : x^2 + y^2 < 1 \}$

Consider the improper integral parametrized by $$a$$:

$I_a := \iint_{D} \frac{dxdy}{(\sqrt{1-x^2-y^2})^{5a}}$

For what real values of $$a$$ does $$I_a$$ converge?