Evaluate $\int\int_R e^{-x-y}dxdy$
where R is the region in the first quadrant which $x\leq y$
Please, help graph the region

Question

Evaluate $\int\int_R e^{-x-y}dxdy$ 
where R is the region in the first quadrant which $x\leq y$
Please, help graph the region

loser66 · Answer

|dw:1467251635357:dw|

loser66 · Answer

It is not hard to find the value of the integral algebraically. However, I would like to know which region is R

loser66 · Answer

To me, region 1 is the correct one.

kainui · Answer

Wait it says $x \le y$. So like x=1 and y=2 is $x\le y$ right?

loser66 · Answer

Yes

kainui · Answer

I'd say that the point (1,2) is in region 1

loser66 · Answer

hehehe... the same method I test for the region. :)

kainui · Answer

seems like a pretty good method to me :)

loser66 · Answer

http://www.math.illinois.edu/~ajh/370/408doubleintegralssol.pdf Problem 7.

sdfgsdfgs · Answer

i say 1 too as $$x \le y$$

loser66 · Answer

@Kainui  I have too much free time, so that I study actuary online. I tried to solve the problem without looking at the solution. However, the solution on the page is not what I got. That is why I post it here.

loser66 · Answer

@sdfgsdfgs  Thank you, friend.

loser66 · Answer

oh, sorry, problem 9

kainui · Answer

That picture is wrong, it doesn't match the bounds on the integral, they even have:

$$\huge \int_{x=0}^\infty \int_{y=x}^\infty$$

Ok the interval y=x to y=infinity is the region you describe, but not the picture drawn, since that's clearly everything above the line y=x like we're saying.

loser66 · Answer

Thank you so much. Ha!! I realize that studying online is not easy at all.

kainui · Answer

Yeah their actual solution of it, the calculation looks fine though haha weird, I guess everyone just makes mistakes time to time

loser66 · Answer

@Kainui  do you have a job?

kainui · Answer

Nope, but I kinda need one.

loser66 · Answer

your major is engineer, right?

kainui · Answer

I have a degree in chemistry, sorta interested in physical chemistry / spectroscopy and organic chemistry and I just love math lol.

loser66 · Answer

By mistake, I got this page. It fits you, I think!! https://www.usajobs.gov/Search/?Keyword=chemistry&Location=Pennsylvania&homeRadPublic=public&search=Search&AutoCompleteSelected=False&CanSeekStatusJobs=False

kainui · Answer

Oooh I'll apply thanks, if you find more stuff feel free to send 'em my way!

loser66 · Answer

ok, by other mistake, I got this page also. hahaha... None of them fits me. http://www.lockheedmartinjobs.com/

loser66 · Answer

good luck, my friend