   Chapter 5.2, Problem 39E ### 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

# Evaluate the integral by interpreting it in terms of areas. ∫ − 4 3 | 1 2 x | d x

To determine

To evaluate: The integral 43|12x|dx by an area interpretation.

Explanation

Given information:

The integral function is 43|12x|dx.

Calculation:

Consider f(x)=|12x|.

Consider y as function of x.

y=f(x) (1)

Substitute |12x| for f(x) in Equation (1).

y=|12x| (2)

Here, Equation (2) represents Equation of line.

The expression for general equation of a line is shown below:

y=mx+c (3)

Here, m is slope of the line and c is the intercept of they-axis.

Compare the Equation (2) and Equation (3).

m=(12) and c=0.

Find the coordinates of (x1,y1) and (x1,y1):

Substitute 4 for x in Equation (2).

y1=|12×(4)|=|2|=2

Substitute 3 for x in Equation (2).

y2=|12×3|=1.5

Therefore, the coordinates (x1,y1) is (4,2) and (x2,y2) is (3,1

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