Chapter 8.4, Problem 33E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Completing the Square In Exercises 33-36, complete the square and find the indefinite integral. ∫ x 4 x − x 2 d x

To determine

To calculate: The solution of the following indefinite integral x4xx2dx.

Explanation

Given:

The indefinite integral âˆ«x4xâˆ’x2dx.

Formula used:

The integration of sinxÂ andÂ cosx are;

âˆ«sinxdx=âˆ’cosx+câˆ«cosxdx=sinx+c

Calculation:

Consider the following expression

4xâˆ’x2

Simplify the expression, to get;

4xâˆ’x2=âˆ’(x2âˆ’4x)=4âˆ’(x2âˆ’4x+4)=4âˆ’(xâˆ’2)2

Now we have;

âˆ«x4xâˆ’x2dx=âˆ«x4âˆ’(xâˆ’2)2dx â€¦â€¦â€¦â€¦.(1)

Substitute xâˆ’2=2sinÎ¸ to get;

xâˆ’2=2sinÎ¸x=2+2sinÎ¸

Now differentiate above expression with respect to x;

dx=2cosÎ¸dÎ¸

Substitute value of x and dx in equation (1)

âˆ«x4âˆ’(xâˆ’2)2dx=âˆ«2(sinÎ¸+1)4âˆ’(sinÎ¸+1)2(2cosÎ¸)dÎ¸âˆ«x4âˆ’

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Through (4, 5), parallel to the x-axis

Single Variable Calculus: Early Transcendentals, Volume I

#### Convert the expressions in Exercises 6584 to power form. x2x

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 1-6, simplify the expression. 1. x2+x2x24

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### âˆ«xâˆ’4dx = âˆ’4xâˆ’5 + C

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Describe the elements of an abstract.

Research Methods for the Behavioral Sciences (MindTap Course List)