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The density of a ball of ice is greatest at the center and decreases with distan

ID: 2873435 • Letter: T

Question

The density of a ball of ice is greatest at the center and decreases with distance from the center of the ball. The ball is 12 centimeters in radius and the density is given by ?(x) grams per cubic centimeter, where x represents the distance from the center of the ball in centimeters.

(a) Write a general Riemann sum that approximates the mass of the ball. Please define all notation that you use; if you use things like ?x or xk (and you should!), give formulas for them.

(b) By taking an appropriate limit of the Riemann sum you found in part (a), write a definite integral giving the mass of the ball. Please state exactly what limit you are using.

Explanation / Answer

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