How do I find a constant k that would result in a valid PDF?

Question

So given the function:

$f(x,y)= \begin{cases} k[20-x-y]&\text{if}\, x > 0, y > 0, x + y < 20\\ 0 x&\text{otherwise} \end{cases}$

I know how to set up the equation using the double integrals, I just don't know what the bounds would be.

Answer 1

$0<x<20$ and $0<y<20-x$, so $$\int_{-\infty}^\infty\int_{-\infty}^\infty f(x,y) dy dx =\int_0^{20}\int_0^{20-x} k[20-x-y] dy dx$$