# Math Help - double integral - converges or diverges

1. ## double integral - converges or diverges

Hey, I've been trying to determine whether this integral converges by saying that it's smaller than e^-[(x+y)^2] over the same region. Then transforming it to polar coordinates and doing the limit I got infinitiy, meaning that the former integral is smaller or equal to infinity.. which doesn't help at all.
It seems like it converges, but I've failed at proving it.

3. the function is positive everywhere. so if $D=\{(x,y) \in \mathbb{R}^2: \ x \leq 0, \ -x \leq y \leq 1-x \},$ then using the fact that $e^a \geq 1+a,$ for all reals $a,$ we'll have:
$\int \int_{\mathbb{R}^2} e^{-(x+y)^4} \ dA > \int \int_D e^{-(x+y)^4} \ dA \geq \int_{-\infty}^0 \int_{-x}^{1-x} (1-(x+y)^4) \ dy \ dx=\infty.$ so the integral is divergent.