   Chapter 6.1, Problem 52E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
23 views

# Area of a Region In Exercises 47-52, find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify your results. y = In  x x 2 ' y = 0 , x = 1 , x = e

To determine

To calculate: The area of the region bounded by graphs of the equations y=lnxx2,y=0, x=1, x=e and then verify the result by using graphing utility.

Explanation

Given Information:

The provided equation is y=lnxx2,y=0, x=1, x=e.

Formula used:

Integration by parts.

When u and v is assumed to be the differentiable functions of x then,

u dv=uvv du

Calculation:

Consider the equation is y=lnxx2,y=0, x=1, x=e.

The graph can be draw with the help of table as,

x0.511.649y500.184

Here the lower limit is x=1 and the upper limit is x=e. So, the area of the bounded regions would be,

Area=1elnxx2 dx

Let u=lnx and dv=1x2dx, then

dv=x2dx

Apply integral on both sides of the above equation as,

dv=x2dxv=x11

Thus, v=1x,

Then differentiate both sides of the equation u=lnx as,

du=d(lnx)du=1xdx

So, du=1xdx

Now apply integration by parts formula

### 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

#### CHECK POINT Let and .Use sets to answer the folowing. 5 .Which of is equals to ?

Mathematical Applications for the Management, Life, and Social Sciences

#### If a X b, show that a E(X) b.

Probability and Statistics for Engineering and the Sciences

#### Improper IntegralsDescribe the different types of improper integrals.

Calculus: Early Transcendental Functions (MindTap Course List)

#### True or False: is conservative.

Study Guide for Stewart's Multivariable Calculus, 8th 