   Chapter 5.4, Problem 63E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The linear density of a rod of length 4 m is given by ρ ( x ) = 9 + 2 x measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

To determine

To find: The total mass of the rod.

Explanation

Given information:

The linear density of the rod is ρ(x)=9+2x.

The length of the rod is 4 m. Hence, the limits are x1=0 and x2=4.

Calculation:

Find the total mass (m) of the rod using the relation:

m=x1x2ρ(x)dx (1)

Here, the linear density function is ρ(x).

Substitute (9+2x) for ρ(x), 0 for x1, and 4 for x2 in Equation (1).

m=04(9+2x)dx (2)

Integrate Equation (2) with respect to x and apply the upper and lower limits

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