   Chapter 3.9, Problem 66E

Chapter
Section
Textbook Problem

# The linear density of a rod of length 1 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.

To determine

To find:

The mass of the rod.

Explanation

1) Concept:

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is, Fx+c, where c is an arbitrary constant.

2) Given:

The length of the rod =1m=100 cm

ρx=1x

3) Calculation:

Let m(x) be the measure of one end of rod.

Consider, ρx=1x

i.e.ρx=dmdx=1x

By taking antiderivative,mx=2x12+C

The initial length is 0 i

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