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…

06:05

Question

Answered step-by-step

Problem 76 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{x^2}{\sqrt{x^2 + 1}}\ 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
Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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

05:55

Evaluate the integral.

…

02:18

Evaluate the integral.

…

01:20

Evaluate the indefinite in…

01:27

Evaluate the definite inte…

00:42

Evaluate the indefinite in…

03:17

Evaluate the integral.
…

07:59

Evaluate the integral.

…

08:55

Evaluate the integral.

…

03:04

Evaluate the integrals.

02:38

Evaluate the integrals.

00:39

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 start this one off by doing the tricks up X equals Santana. Then if this is our ex Lady X Seek and square Seita data, so are in a girl can be written while first we see there's a X squared that's ten square and then we see t X. But we were re evaluated that that's just c can't square. And then in the denominator we have X squared plus one in the radical, usually one of Europe with a green identities. We could write that a c can't square and they're seeking We could cross off that seeking in the denominator. And we could also rewrite tangent as seek and squared minus one. So we're left over with Tangent Square here so that seek and square minus one and then we still have one worse he cannot hear. So that's in a girl seeking Kim theta d theta minus in a girl seek and Dana Dana. Now this second and our girl we memorized by now this is just a trigger and her girl here. But for the first one, we could do an aggression by parts here, so I won't go over the whole details here But you could take you to B. C can't data and then take TV to be seeking square theater. And so, for the first in a girl, when we evaluate that for the sea can cute and then we have one half at lend. So this is all for be integral the sea cans in a third hour. That was what we wrote on the previous page. And then here we subtracted in a girls he can't, which is natural log of seek and eight of those Xanterra and was good and add that constancy. And so this term here was just the term on the previous page seek and data and that out there, she had a date or two. So here just combined thes two terms here and we're basically finished after we draw the triangle. Of course. So we thought a little work to do here. Okay, so now we draw a triangle. There's our angle data. And from the previous page we had tangent was defined as just X. You're getting sloppy here. We had X equals Tan Dana, which we could also write his ex over one so opposite, over adjacent and then used with agreeing to Europe to find the high part news. So here, But all we have to do that was fine. See Canon Tangent, where no tension is just X and then c can of data is just hype on news over adjacent. So it's just the radical. So let's just go ahead and replace. He can't intention on the next page. So they're seeking in Tan. And then here we have the one half and the natural log of C can't plus hand. So there's he can't right there. The radical that we just found on the previous page tangent was X. Let's add that concept of integration, see? And there's a

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
192
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
82
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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

05:55

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

02:18

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

01:20

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

01:27

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

00:42

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

03:17

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

07:59

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

08:55

Evaluate the integral. $ \displaystyle \int_0^1 \sqrt{x - x^2}\ dx $

03:04

Evaluate the integrals. \begin{equation}\int_{1}^{\sqrt{2}} x 2^{\left(x^{2}\r…

02:38

Evaluate the integrals. $$\int_{1}^{\sqrt{2}} x 2^{\left(x^{2}\right)} d x$$

00:39

Evaluate the integral. $ \displaystyle \int^4_1 \frac{2 + x^2}{\sqrt{x}} \,d…

04:51

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

01:31

The original size of a soft drink is 12 fl 0z, with population standard devi…

08:21

y" 10y' + 9y = 5t,
y(o) = -1
y (0) = 2

03:36

Find all solutions, y(t) , to the differential equation
dy ~y =3 dt

05:08

If P dollars is borrowed at a monthly interest rate and you want to pay it o…

01:12

multiple of I Do not use calculator: Convert each degree measure to radian m…

01:21

Consider the figure. Find AB if BC = 3, BD = 5, and AD = 4
AB = 3v 2

02:21

Consider the following limit of Riemann sums of a function f on [a,b]: Ident…

04:41

Find the sixth Taylor polynomial of f(x) 6e-x at x = 0.
Pe(x)
Use your…

01:42

Question 1
Is this value from a discrete or continuous data set:
The a…

03:29

The temperature in an auditorium is given by T = x + y2 _ z A mosquito locat…

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
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started