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Multivariable CalculusChallengeTriple Integrals & Coordinate Systems

Triple Integrals & Coordinate Systems · Challenge problem

Let EE be the solid ball x2+y2+z2≤2zx^2 + y^2 + z^2 \le 2z. Evaluate ∭E(x2+y2+z2) dV\displaystyle\iiint_E (x^2 + y^2 + z^2)\,dV. Give your answer in terms of π\pi.