This is probably a silly question but I've never seen this notation:
For a > 0, compute
$$\int\int_{x/y \leq a} 2e^{-(2x+y)} dx dy$$
What is $x/y \leq a$ there for?
This is from my statistics homework.
2026-05-15 07:36:50.1778830610
Confusion about integration notation
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$\dfrac{x}{y}\le a$, or $y\ge\dfrac{x}{a}$, defines a region in the $x$-$y$ plane, equivalent to the half-plane that lies below (and including) the line $y=\dfrac{x}{a}$.
What this amounts to is you are setting up a double integral to be evaluated over a region $R$ described by $$R:=\left\{(x,y)\mid -\infty< x<\infty,\, -\infty<y\le \frac{x}{a}\right\}$$