A city is built around a circular lake that has a radius of 1 mile. The population density of the city is f (r) people per square mile, where r is the distance from thecenter of the lake, in miles. Which of the following expressions gives the number of people who live within 1 mile of the lake?

Question

anonymous · Answer

It says the answer is:
$$2 pi \int\limits_{1}^{2}rf(r)dr$$

anonymous · Answer

yes, that's it... Do you understand it?

anonymous · Answer

No

dumbcow · Answer

to get population you need to multiply f(r) by total area
one way of getting area is adding up all the circumferences

anonymous · Answer

How do I determine the limits of integration here?

anonymous · Answer

its between the lake and the boundary... 1 for boundary of lake and 2 for one mile from it...

dumbcow · Answer

people farthest out are 1 mile away from lake but edge of lake is 1 mile away from center
thus 2 miles away....r=2
people closest are on lake edge, one mile away from center ....r=1

anonymous · Answer

(boundary of lake is one mile away from its center)

anonymous · Answer

Thanks guys!