   Chapter 5, Problem 40RE ### 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, if it exists. ∫ 0 4 | x − 1 | d x

To determine

The value of the integral function.

Explanation

Given information:

The integral function is 04|x1|dx.

The region lies between x=0 and x=4.

Observation:

Split the integral limits into two parts, with the function (x1)>0 and the other limits with the function (x1)<0 to get the absolute value of the function.

Express the function |x1| as shown below:

|x1|={x1 if(x1)>0(x1) if(x1)<0 (1)

Calculate the value of limit x for the condition (x1)>0 as shown below:

(x1)>0x>1x>1

Calculate the value of limit x for the condition (x24)<0 as shown below:

(x1)<0x<1x<1

Rearrange Equation (1) using the limits of x, to get the absolute value of function as shown below:

|x1|={x1 if <

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