How to perform a double integration Suppose you are trying to find the integral of $x^2 + y^2$ such that $(x^2 + y^2) \leq 1$. How would you do this?
Attempt: I know the radius is 1 but I am stuck when trying to determine the limits of integration. 

Let's take advantage of symmetry and stay in the first quadrant. Integrate as follows
$$4\int_0^1 \int_0^{\sqrt{1 - x^2}}(x^2 + y^2)\,dy\,dx$$
We obtain the limits of integration because the first quadrant of the unit disk is described by the inequalities $0\le x \le 1$ and $0\le y \le \sqrt{1 - x^2}$.
