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Multivariable CalculusHardTriple Integrals & Coordinate Systems

Triple Integrals & Coordinate Systems · Hard problem

Evaluate ∫01 ⁣∫01−x2 ⁣∫x2+y22−x2−y2xy dz dy dx\displaystyle\int_0^1\!\int_0^{\sqrt{1 - x^2}}\!\int_{\sqrt{x^2 + y^2}}^{\sqrt{2 - x^2 - y^2}} xy\,dz\,dy\,dx. Give an exact answer.