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Multivariable CalculusSuperchallengeTriple Integrals & Coordinate Systems

Triple Integrals & Coordinate Systems · Superchallenge problem

Let BB be the solid unit ball x2+y2+z2≤1x^2 + y^2 + z^2 \le 1 and Q=(0,0,2)Q = (0,0,2). Evaluate ∭BdVx2+y2+(z−2)2\displaystyle\iiint_B \dfrac{dV}{\sqrt{x^2 + y^2 + (z-2)^2}}, the gravitational potential of the ball at QQ (up to a constant). Give your answer in terms of π\pi.