9367 Q63

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

9367 Q63

Postby yoyobarn » Wed Dec 21, 2011 4:25 am

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.

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

Re: 9367 Q63

Postby fireandgladstone » Wed Dec 21, 2011 8:03 am

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

Re: 9367 Q63

Postby yoyobarn » Wed Dec 21, 2011 9:11 am

Ok thanks a lot.




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