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

The region bounded by the given curves is rotated…

02:03

Question

Answered step-by-step

Problem 41 Hard Difficulty

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

$ x^2 + (y - 1)^2 = 1 $ ; about the y-axis


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Amrita Bhasin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

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

More Answers

02:53

WZ

Wen Zheng

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 3

Volumes by Cylindrical Shells

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

04:05

The region bounded by the …

02:25

The region bounded by the …

03:40

The region bounded by the …

03:14

The region bounded by the …

01:41

The region bounded by the …

02:03

The region bounded by the …

Watch More Solved Questions in Chapter 6

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

Video Transcript

okay, we know it's specified in the problem. The radius is X and the height is two time squirt of one minus X scored. Which means we're gonna be putting into the general formula, which is two pi times the integral from 01 off the height times the radius D of acts 01 are two bounds. Therefore, we end up with V is gonna be four pi times integral from 01 ax time scored of one less ex squirt. Where did the two go? You ask? Well, we remember the height was two time squared of our mess. X squared. I simply pulled the two out on the outside. It's a constant multiplied it by the original two pi toe end up with four pi on the outside Just a simple five days. Now we know in this context we can actually use U substitution, which you learned in a previous chapter. If you is one minus X squared than taking d'you, we end up with d'you. The derivative is negative to axe de axe. So what this means is that negative 1/2 to you is ex dx other words gonna be dividing four by two which means we end up with and remember, it's actually dividing for by negative, too, because it was negative. Two ex Texas do you So negative two pi times the integral from 10 There flips now because of the nature of the fact that we've taken u substitution. We've got negative value. Do the power rule In order to integrate increased exports by one divide by the new exponents, we end up with four pi divided by three

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
95
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Recommended Videos

04:05

The region bounded by the given curves is rotated about the specified axis. Fin…

02:25

The region bounded by the given curves is rotated about the specified axis. Fin…

03:40

The region bounded by the given curves is rotated about the specified axis. Fin…

03:14

The region bounded by the given curves is rotated about the specified axis Find…

01:41

The region bounded by the given curves is rotated about the specified axis. Fin…

02:03

The region bounded by the given curves is rotated about the specified axis. Fin…

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