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

Find the volume of the resulting solid if the reg…

10:13

Question

Answered step-by-step

Problem 65 Hard Difficulty

Find the area of the region under the given curve from 1 to 2.

$ y = \dfrac{x^2 + 1}{3x - x^2} $


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 4

Integration of Rational Functions by Partial Fractions

Related Topics

Integration Techniques

Discussion

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

Missouri State University

Caleb Elmore

Baylor 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

03:26

Find the area of the regio…

04:49

Find the area of the regio…

02:04

Find the area of the regio…

01:28

Find the area of the regio…

03:44

Find the area of the regio…

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

Video Transcript

this problem is asking for the integral from one to two of this function. And let me rewrite this denominator by factoring chips just three minus X. That's the area under the curve from one to two. So here the numerator and denominator of the same degree. They're both degree too. So we should along the vision here. So go to the side and do long division because we always should do this before a partial fractions. It's minus three X and then we have three. X Plus one is our remainder. So using this long division, I can rewrite this integral negative one and then three X plus one x three minus x t x And then we'LL go out and do partial fraction to composition on this fraction here using what the author calls Case one. So here we have a three minus X. So it's good and multiply both sides of this by distant dominator here on the left that on the right, so much factor on the X and we see that b minus a must be three and three a must be won. So we get that moves. So here we have one equals three soft ray and then used in this equation. Here we have B minus a third is three or weaken right that is nine over three. So soft for be there. Just add that one over three over. So we have our A and B. Now let's just go ahead and plug those in Now. We could replace this fraction here with the partial fraction. And let's write that on the next page. Once a two, we have the negative one from a long division and then for a partial fractions. That's our area. Now let's go ahead and evaluate these inner rules. If this last one. If this is bothering you with the three minus X, feel free to do it. Use up here. You could do U equals three minus six and to uni equals negative DX. That should work. So let's integrate these three. The first one just is minus X for the next one. Natural log. Absolute value X and for the last one, ten over three with a minus natural log. Absolute value three minus X, and you could see the negative is coming from the use of. And don't forget our UN points wanted to it's good and plug those in one at a time. Ellen. One there. We know that zero Ellen one. That's also zero minus ten over three. Ellen, too, And then just go out and simplify this eleven over three. Natural onto. That's our answer.

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
43
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Caleb Elmore

Baylor 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

03:26

Find the area of the region under the given curve from 1 to 2. $ y = \dfrac{…

04:49

Find the area of the region under the given curve from 1 to $2 .$ $y=\frac{1}{x…

02:04

Find the area of the region under the curve y = 1 /x^3 + x, 1 ≤ x ≤ 2

01:28

Find the area of the region between the curves. $$y=x^{3} \text { and } y=2 x^{…

03:44

Find the area of the region between the curve $y=3-x^{2}$ and the line $y=-1$ …

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