Prove of the complicated integral

[shayaan_musta]

Hi experts!

How to prove this integral?

\frac{2}{e^{5}}\leq\int\int_{D}e^{-(x^{2}+y^{2})}dxdy\leq2
on
D=[0,1] and [0,2]

Here D is subscript of the 2nd integral.

I seriously have no idea how to start. I am 100% blank with this question.

Thanks in advance.

 

[micromass]

What is the maximum/minimum value that e^{-(x^2+y^2)} can attain??

 

[JG89]

Why not just calculate the integral? The rectangle (0,1) x (0,2) is diffeomorphic to a circle (or the circle minus a set of measure zero) so use the change of variables theorem.