Let W be the ball of radius R in R3 centered at the orig
Question and Solution
Let W 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
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Let W 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 sphere W is equal to d = 6R/5. Hint: Show that d = 1 4 3?R3 2? ?=0 R ?=0 ? ?=0 ?2 sin ? R2 + ?2 ? 2?R cos ? d? d? d? and evaluate
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