   Chapter 5.2, Problem 40E ### 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. ∫ 0 1 | 2 x − 1 | d x

To determine

To evaluate: The integral function 01|2x1|dx by interpreting it in terms of areas.

Explanation

Given information:

The integral function is 01|2x1|dx.

Calculation:

Suppose that the lower limit of the function as x1 and upper limit of the function as x2

Consider the function f(x)=|2x1|, with lower limit x1=0 and upper limit x2=1

Consider y as a function of x as given below:

y=f(x) (1)

Substitute |2x1| for f(x) in Equation (1).

y=|2x1| (2)

Calculate the coordinates (x1,y1) and (x2,y2) using Equation (2).

Calculate y1 using Equation (2).

Substitute 0 for x in Equation (2)

y1=|2x1|=|2×01|=|1|=1

Calculate y2 using Equation (2).

Substitute 1 for x in Equation (2)

y2=|2x1|=|2×11|=1

Consider the coordinates (x1,y1) as (0,1) and (x2,y2) as (1,1)

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