   Chapter 5.4, Problem 46E ### 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 3 π / 2 | sin x | d x

To determine

To calculate: The absolute value of the integral.

Explanation

Given information:

The integral function is 03π2|sinx|dx.

The region lies between x=0 and x=3π2.

Observation:

Split the integral limits into two parts, with the function |sinx|0 and the other limits with the function |sinx|<0 to get the absolute value of the function.

Express the function |sinx| as shown below:

|sinx|={sinx if|sinx|0sinx if|sinx|<0 (1)

Calculate the value of limit x for the condition |sinx|0 as shown below:

sinx0x<π

Calculate the value of limit x for the condition |sinx|<0 as shown below:

sinx<0x>π

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

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