I am stuck with this problem:
$$\int \int_Q e^{-x-y}dA$$ where Q is the first quadrant of the XY plane.
I then rewrite it as $\int_0^ \infty \int_0 ^\infty e^{-x-y}dxdy$. So far so good. If we start with the inner integral we get $\int_0 ^\infty e^{-x-y}dx = -[e^{u}]_0^{-\infty}=-1$. Then when we get back to the double integral, we now got $\int_0^ \infty-1dy=[-y]_0^\infty=-\infty$. However the correct answer is 1. What am I doing wrong? I have watched multiple similar problems and I understand the concepts overall but this particular one is different.