LetW be the ball of radius R in R 3 centered at the origin, and let P
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LetW be the ball of radius R in R3 centered at the origin, and let P = (0, 0, R) be the North Pole. Let dP(x, y, z) be the distance from P to (x, y, z). Show that the average value of dP over the ballW is equal to d = 6R/5. Show that
and evaluate.
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