http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 30 Jul 2014 09:17:18 -0500http://calc3.askbot.com/question/198/quiz-3-question-1/I'm having an issue on quiz 3, question 1. What I got was.. $$\int _0 ^{2\pi} \int _0^1 e^{-r^2} $$ $$= \int _0 ^{2\pi} e ^{-r^2} r \delta \theta \bigg |_0 ^1$$ $$= \int _0 ^{2\pi} e^{-1} \delta \theta $$ $$= 2\pi e^{-1} $$ Which I know isn't right, but I'm not sure where exactly I went wrong?TiffanyWed, 30 Jul 2014 09:17:18 -0500http://calc3.askbot.com/question/198/http://calc3.askbot.com/question/169/setting-up-exponential-function-in-cartesian-coordinates/I am hoping for some help looking at the exponential function in Cartesian land. If we are given $e^{-(x^2+y^2)}$ and asked to set this up over the domain of a disk of radius R both in polar and Cartesian coordinates, is this what polar would look like? $$\int_0^{2\pi}\int_0^R e^{-(r^2)}rdrd\theta$$ In turn, is this what the Cartesian set-up would look like? $$\int_{-R}^R\int_0^\sqrt{R-x^2} e^{-(x^2+y^2)} dydx$$ Any help or comments would be great. Thanks! **COMMENT** - Thanks Gear Junky, that makes sense. I am struggling to remember to visualize the projection onto the xy plane. As far as evaluating it, I would definitely evaluate the polar coordinates. I was just practicing because he said we may have a problem like this on the quiz to set up in both but evaluate one. ChristinaThu, 24 Jul 2014 14:52:49 -0500http://calc3.askbot.com/question/169/