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I'm having an issue on quiz 3, question 1. What I got was..

$$\int _0 ^{2\pi} \int _0^1 e^{-r^2} $$ $$= \int _0 ^{2\pi} e ^{-r^2} r \delta \theta \bigg |$$ $$= \int _0 ^{2\pi} e^{-1} \delta \ theta $$ $$= 2\pi e^{-1} $$

Which I know isn't right, but I'm not sure where exactly I went wrong?

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 \theta $$ $$= 2\pi e^{-1} $$

Which I know isn't right, but I'm not sure where exactly I went wrong?