   Chapter 5.4, Problem 44E ### 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. ∫ 0 2 | 2 x − 1 | d x

To determine

To calculate: The absolute value of the integral function.

Explanation

Given information:

The integral function is 02|2x1|dx.

The region lies between x=0 and x=2.

Observation:

Split the integral limits into two parts, one with the function 2x10 and the other limits with the function 2x1<0 to get the absolute value of the function.

Express the function |2x1| as shown below:

|2x1|={2x1 if2x10(2x1) if2x1<0 (1)

Calculate the value of limit x for the condition 2x10 as shown below:

2x102x1x12

Calculate the value of limit x for the condition 2x1<0 as shown below:

2x1<02x<1x<12

Rearrange Equation (1) using the limits of x to get the absolute value of function.

|2x1|={2x1 ifx1212x ifx<12 (2)

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

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