Multivariable Function as Product of Two Functions
If you can write a multivariable function as the product of two functions, one of which is defined by $x$ and the other $y$, integrating it becomes much easier. You can simply rewrite the function $f(x,y) = g(x)h(y)$ and so you can simply do the following operation:
$$ \int_a^b\int_c^df(x,y)dydx=\int_a^bg(x)dx\int_c^dh(y)dy $$