Double integrals over general regions Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier. $$\int\int_{D}{ydA}, \text{$D$ is bounded by $y=x-2, x=y^2$}$$
I'm having trouble with setting up the integral for both type I and type 2 and choosing which one would be easier. I'm sure I'll be able to integrate it with no problem, but setting them up is where I would need some help. 

A type 2 region will work. Observe the graph if done as a type 2:

$$\int_a^b\int_{h_1(y)}^{h_2(y)}y\,dx\,dy$$
First you need to find where the two intersect:
$$y+2=y^2$$
$$y^2-y-2=0$$
$$y=-1;y=2$$
$$(1,-1),(4,2)$$
It is clear that the bounds are as follows:
$$\begin{align}
h_1(y)&=y^2 \\
h_2(y)&=y+2 \\
a&=-1 \\
b&=2
\end{align}$$
