Science:Math Exam Resources/Courses/MATH103/April 2009/Question 05 (c)/Statement

A carrot has the shape formed by revolving the region under the graph of

$f(x)={\sqrt {14-x}}$

for $0\leq x\leq 12$ cm about the x axis. The concentration of vitamin A is found to vary in the carrot with x according to

$c(x)={\frac {1}{12}}e^{-x/12}{\frac {\text{mg}}{{\text{cm}}^{3}}}$

You want to cut the carrot at a certain value of x, obtaining two pieces of equal volume. How many centimeters from x = 0 do you have to cut?