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9367 Q63

Posted: Wed Dec 21, 2011 4:25 am
by yoyobarn
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.

Re: 9367 Q63

Posted: Wed Dec 21, 2011 8:03 am
by fireandgladstone
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.

Re: 9367 Q63

Posted: Wed Dec 21, 2011 9:11 am
by yoyobarn
Ok thanks a lot.