Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Evaluate the integral. $ \displaystyle \int \f…

03:42

Question

Answered step-by-step

Problem 69 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int_1^{\sqrt{3}} \frac{\sqrt{1 + x^2}}{x^2}\ dx $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

JH
J Hardin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by J Hardin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

05:00

Evaluate the integral.

…

01:15

Evaluate the definite inte…

01:04

Evaluate the indefinite in…

03:29

Evaluate the integral.

…

05:55

Evaluate the integral.

…

01:48

Evaluate the integral.
…

01:27

Evaluate the definite inte…

04:53

Evaluate the following def…

00:53

Evaluate the integral by m…

02:18

Evaluate the integral.

…

04:18

Evaluate the integral.
…

00:38

Evaluate the integral.
…

04:51

Find the Integral of \int …

Watch More Solved Questions in Chapter 7

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84

Video Transcript

Let's use integration by parts for this one. Let's go ahead and take you to be the Numerator Explorer plus one inside the radical. Then do you go ahead and use the chain rule here from Kokkalis and then simplify should get this for do you and then we're left over with DV equals less right as X to the minus two and this gives us that the so here you have to integrate to use the power rule. Negative one over X. Yeah, so they're recalled the formula UV minus integral video. So let's go ahead and plug in Are you and being and let's not forget the limits here. This is a definite our world's on our problem. We will still be using these limits here. So we have you times be that will give us That's a negative in front of the radical oops over X And then we plug in one and then route three. So that's are you. Times be there this term over here and then now will do the subtraction And then we have this term over here, so we have negative and then we have inner girl and then V and then we have, do you as well. So let's go ahead and write that. So VD you that gives us negative one over X and then X over square root, X squared plus one. And here we see that we can cancel these minuses that gives us a plus. And then we could cancel those exes as well. And we just have the integral of one over this square. Next plus one, you can use a trick. So for this one, go ahead and take X to be tan data to evaluate the tricks up there. And let's not forget our limits. One blue three still, just as the original problem. So here I go, after using that tricks up and then for all so we could plug in these limits into this expression. So plug in room three first and then because of this minus sign here, we add that's plugging in one right there and then after in aerating this thing, using the tricks of and then going back in terms of X, this's our anti derivative. And then we still have the same end points after sense for back in X. So it's going a lot Next page here. The last thing to do is this toe plug in thes two values for X into this expression here, and that's a threat. And so, after simplifying we have room to that's from the root to over one square before is too. So that's negative to O. R. Room three and then natural Log to plus through three and then minus natural log one plus square or two. And we do not need absolute value here because these terms are both positive and that's a finalist.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
67
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
44
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

05:00

Evaluate the integral. $ \displaystyle \int \frac{1}{x^3 \sqrt{x^2 - 1}}\ dx…

01:15

Evaluate the definite integral. $\int_{1}^{\sqrt{3}} \frac{d x}{x^{2}+1}$

01:04

Evaluate the indefinite integral. $ \displaystyle \int x^3 \sqrt{x^2 + 1} \…

03:29

Evaluate the integral. $ \displaystyle \int \frac{\sqrt{x}}{1 + x^3}\ dx $

05:55

Evaluate the integral. $ \displaystyle \int \frac{\sqrt{1 + x^2}}{x}\ dx $

01:48

Evaluate the integral. $$\int_{1}^{3}(2-\sqrt{x})^{2} d x$$

01:27

Evaluate the definite integral. $ \displaystyle \int^2_1 x\sqrt{x - 1} \, d…

04:53

Evaluate the following definite $$\int_{1 / \sqrt{3}}^{1} \frac{d x}{x^{2} \sqr…

00:53

Evaluate the integral by making the given substitution. $ \displaystyle \in…

02:18

Evaluate the integral. $ \displaystyle \int \frac{x}{\sqrt{1 + x^2}}\ dx $

04:18

Evaluate the integral. $$ \int \frac{1}{x^{3} \sqrt{x^{2}-1}} d x $$

00:38

Evaluate the integral. $$\int_{1}^{\sqrt{2}} \frac{x d x}{3+x^{4}}$$

04:51

Find the Integral of \int \frac{1}{\sqrt{1+x^2}}dx
Additional Mathematics Questions

01:23

A grocer's weekly profit from the sale of two brands of orange juice is…

03:44

Given the demand function q = (7500 750p)? . Determine whether demand is ela…

03:17

Ifn is a known positive integer; for what value of k is fk z"-'dx …

01:55

The management of National Electric has determined that the daily marginal c…

06:13

In a poll of 591 human resource professionals, 45.3% said that body piercing…

02:02

Rcler W 621191041 uolisano and and and Exlibit 1 991 0T; 8 025 36 10 3 39 er…

01:22

For the given binomial sample size and null-hypothesized value of Po determi…

03:32

Question 17 (1 point) You are the producer of a television quiz show that gi…

06:47

Technetium-99 99mTc _ radionuclide used widely in nuclear medicine _ 99mTc c…

02:25

In a study of fast food drive-through orders, McDonald s had 53 orders that …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started