## 9367 Q63

Forum for the GRE subject test in mathematics.
yoyobarn
Posts: 80
Joined: Sun Dec 19, 2010 7:01 am

### 9367 Q63

Let R be the circular region of the xy-plane with center at the origin and radius 2.
Then $\int\int_R{e^{-(x^2+y^2)}dx dy=$

I fell into the trap and answered:
$=\int\int e^{-4}dA=4\pi e^{-4}$

May I know what is wrong with the above approach, and how do we get the correct answer?

Thanks a lot.

Posts: 27
Joined: Sun Oct 17, 2010 4:57 am

### Re: 9367 Q63

They're asking for the integral over the whole circle, not just the perimeter. Anytime you see "circular region" on the GRE with x^2+y^2 somewhere in the integrand you should think of polar coordinates.

yoyobarn
Posts: 80
Joined: Sun Dec 19, 2010 7:01 am

Ok thanks a lot.