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Multivariable CalculusEasyTriple Integrals & Coordinate Systems

Triple Integrals & Coordinate Systems · Easy problem

Evaluate the spherical-coordinate integral ∫02π ⁣∫0π ⁣∫02ρ2sin⁡ϕ dρ dϕ dθ\displaystyle\int_0^{2\pi}\!\int_0^{\pi}\!\int_0^2 \rho^2\sin\phi\,d\rho\,d\phi\,d\theta. Give your answer in terms of π\pi.