   Chapter 8.4, Problem 34E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The required solution of the indefinite integral x22xx2dx.

Explanation

Given:

The indefinite integral is x22xx2dx.

Formula used:

Integration identity, sinθ=cosθ+c

Calculation:

Consider the expression, 2xx2

The expression can be written as;

2xx2=(x22x)=1(x22x+1)=1(x1)2

So, the indefinite integral becomes;

x22xx2dx=x21(x1)2dx

Because 1(x1)2 is of the form a2x2. So, make use of the trigonometric solution, x1=sinθ to solve it as shown in figure.

The derivative comes out to be:

dx=cosθdθ

Substitute x1=sinθ and dx=cosθdθ in the integration as;

x22xx2dx=x21(x1)2dx=(1+sinθ)21sinθ2cos

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

Solve the equations in Exercises 112 for x (mentally, if possible). x+1=2x+2

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 32xx2dx

Calculus (MindTap Course List)

In problems 45-62, perform the indicated operations and simplify. 51.

Mathematical Applications for the Management, Life, and Social Sciences

True or False: n=1n+n3n2/3+n3/2+1 is a convergent series.

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