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Question-141856




Question Number 141856 by rs4089 last updated on 24/May/21
Answered by TheSupreme last updated on 24/May/21
x=ρsin(ϕ)cos(θ)  y=ρsin(ϕ)sin(θ)  z=ρcos(θ)  det∣J∣=ρ^2 sin(ϕ)  ∫∫∫sin(ϕ)dϕdθdρ=  ∫_0 ^π sin(ϕ)dϕ∙2πa=4πa
$${x}=\rho{sin}\left(\varphi\right){cos}\left(\theta\right) \\ $$$${y}=\rho{sin}\left(\varphi\right){sin}\left(\theta\right) \\ $$$${z}=\rho{cos}\left(\theta\right) \\ $$$${det}\mid{J}\mid=\rho^{\mathrm{2}} {sin}\left(\varphi\right) \\ $$$$\int\int\int{sin}\left(\varphi\right){d}\varphi{d}\theta{d}\rho= \\ $$$$\int_{\mathrm{0}} ^{\pi} {sin}\left(\varphi\right){d}\varphi\centerdot\mathrm{2}\pi{a}=\mathrm{4}\pi{a} \\ $$

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