Multiple integrals

A double integral over a rectangle splits into two single integrals done one after the other. For $R=[a,b]imes[c,d]$, write ${\iint }_{R}f(x,y)dA={\int }_c^d{\int }_a^{b}f(x,y)dxdy$. Integrate with respect to $x$ first, treating $y$ as a constant, then integrate the result with respect to $y$. For non-rectangular regions, describe the region with inequalities and choose an order so the inner limits may depend on the outer variable but not the other way around.