   Chapter 5.5, Problem 65E ### 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 definite integral. ∫ 0 a x x 2 + a 2   d x   ( a > 0 )

To determine

To evaluate: The definite integral.

Explanation

Given:

The definite integral function is 0axx2+a2dx,(a>0).

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

Calculation:

Consider u=x2+a2 (1)

Differentiate both sides of the Equation (1).

du=2xdxxdx=12du

Calculate the lower limit value of u using Equation (1).

Substitute 0for x in Equation (1).

u=(0)2+a2=a2

Calculate the upper limit value of u using Equation (1).

Substitute a for x in Equation (1).

u=(a)2+a2=2a2

The definite integral function is,

0axx2+a2dx (2)

Apply lower and upper limits for u in Equation (2).

Substitute u for (x2+a2) and (12du) for (xdx) in Equation (2).

0axx2+a2dx=a22a2u(12du)=12a22a2udu=12a22a2u12du (3)

Integrate Equation (3)

### 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 126. (x2+1)(x+1)43(x+1)73=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find the median for the following set of scores: 1, 9, 3, 6, 4, 3, 11, 10

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### In Problems 7-34, perform the indicated operations and simplify. 22.

Mathematical Applications for the Management, Life, and Social Sciences 