A carrot has the shape formed by revolving the region under the graph of f(x)=sqrt(14-x) for 0=<x=<12 cm about the x axis. The concentration of vitamin A is found to vary in the carrot with x according to c(x) = 1/12e^(-x/12) mg/cm^3.
a) What is the volume of the carrot?
b) What is the total amount of vitamin A in the carrot?
c) You want to cut the carrot at a certain value of x, obtaining two pieces of equal volume. How many cm from x=0 do you have to cut?
I got 96pi for part a. My integral for part b is the integral from zero to twelve of pi(14-x)*c(x)*dx. I can't seem to solve that. Is that even the right integral? Or should the integral be of 2pi*sqrt(14-x)*c(x)*dx?