9367 Q63

[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.

[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.

[yoyobarn]

Ok thanks a lot.