Expert: Paul Klarreich - 11/17/2008

Question
The linear density of a rod of length 9 m is given by ρ(x) = 1 / √x, in grams per centimeter, where x is measured in centimeters from one end of the rod. Find the mass of the rod.

I found the antiderivative: m= 2x^(1/2)+ C. I plugged in 9 for x but I don't know how to find C.

Answer
Questioner:   Kathleen
Category:  Calculus
Private:  No
 
Subject:  Linear Density
Question:  The linear density of a rod of length 9 m is given by ρ(x) = 1 / √x, in grams per centimeter, where x is measured in centimeters from one end of the rod. Find the mass of the rod.

I found the antiderivative: m= 2x^(1/2)+ C. I plugged in 9 for x but I don't know how to find C.
...........................
Hi, Kathleen,

You don't find C.  This is a definite integral.  You want:

{900
|    x^(-1/2) dx
}0

= 2x^1/2 from 0 to 900

= 2(30) = 60.

(That is not the only way to look at it, of course.)\