This is the second question on my calculus PSET:

2. 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 p(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 you use; that is, if you use things like Ax or xk (and you should!), give formulas for them. You may want to look back at Problem Set 01, especially at #2 and #4. (b) By taking an appropriate limit of the Riemann sum you found in (a), write a definite integral giving the mass of the ball. Please state exactly what limit you are using