Let R be the circular region of the xyplane 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.
9367 Q63

 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.