If I am given a double integral question like
$$\iint_D y\cos (xy) \,dA,$$
where
$$D = \{(x, y) \mid 2 \leq x\leq 3, 0\leq y\leq \pi/2\}.$$
The question is, how do I know the order of $dA$. Is it $(dxdy)$ or $(dydx)$. What is the general rule of thumb? Secondly, how do I know where to place the limits of integration? Is it $$ \int_{0}^{\pi/2} \int_2^3 y\cos (xy) ?? $$ or is it $$ \int_2^3 \int_{0}^{\pi/2} y\cos (xy) ?? $$
Tip for order of $dA$ check at this link.
Next, the limits of integration is easy to recognize thanks to Fubini's Theorem.