Question Number 220976 by SdC355 last updated on 21/May/25
![∫_(−∞) ^( +∞) ∫_(−∞) ^( +∞) e^(−(x^2 +y^2 )) dV →∫_0 ^( 2π) ∫_0 ^( ∞) r∙e^(−r^2 ) drdθ=π i can′t understand domain of integration I=(−∞,∞)×(−∞,∞) → I_J =[0,∞)×[0,2π].....](https://www.tinkutara.com/question/Q220976.png)
$$\int_{−\infty} ^{\:+\infty} \int_{−\infty} ^{\:+\infty} \:{e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} \mathrm{d}{V}\:\rightarrow\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \int_{\mathrm{0}} ^{\:\infty} \:{r}\centerdot{e}^{−{r}^{\mathrm{2}} } \mathrm{d}{r}\mathrm{d}\theta=\pi \\ $$$$\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{understand}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{integration} \\ $$$${I}=\left(−\infty,\infty\right)×\left(−\infty,\infty\right)\:\rightarrow\:{I}_{{J}} =\left[\mathrm{0},\infty\right)×\left[\mathrm{0},\mathrm{2}\pi\right]….. \\ $$