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 given curve is rotated about the y-axis. Find…

01:26

Question

Answered step-by-step

Problem 17 Hard Difficulty

The given curve is rotated about the y-axis. Find the area of the resulting surface.

$ x = \sqrt{a^2 - y^2} $ , $ 0 \le y \le \frac{a}{2} $


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

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 2

Area of a Surface of Revolution

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

02:50

The given curve is rotated…

03:11

The given curve is rotated…

01:32

The given curve is rotated…

05:45

Find the exact area of the…

01:18

Find the exact area of the…

01:27

Find the exact area of the…

01:17

Find the exact area of the…

0:00

Find the exact area of the…

05:41

The given curve is rotated…

01:41

The given curve is rotated…

06:27

The given curve is rotated…

02:11

Find the exact area of the…

Watch More Solved Questions in Chapter 8

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

Video Transcript

we know the first thing you can do is we can find the derivative of X with respect a Y. In other words, we can write negative Why over square root of any squared minus y square Again, we writing this in terms of why Which means now when we plugged into our and to grow we have the bounds from zero to a over to and we have square root of a squared minus four I squared, which we have over here times a squared over a squared minus wife's word. Do you? Why? And this was from the original problem. This part which means this simplifies to two pi times integral from zero over to squirt of a squared, which is just a the other stuff cancels out the skirt and squared, cancels out this simple fires taking the intro a of why, from zero to a divided by two, it's at the point. Now we can plug in to pi eight times over to minus zero. Is pi a square

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

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Recommended Videos

02:50

The given curve is rotated about the $y$ -axis. Find the area of the resulting …

03:11

The given curve is rotated about the y-axis. Find the area of the resulting sur…

01:32

The given curve is rotated about the y-axis. Find the area of the resulting sur…

05:45

Find the exact area of the surface obtained by rotating the curve about the $x$…

01:18

Find the exact area of the surface obtained by rotating the curve about the x-a…

01:27

Find the exact area of the surface obtained by rotating the curve about the x-a…

01:17

Find the exact area of the surface obtained by rotating the curve about the $x$…

0:00

Find the exact area of the surface obtained by rotating the given curve about t…

05:41

The given curve is rotated about the $y$ -axis. Find the area of the resulting …

01:41

The given curve is rotated about the y-axis. Find the area of the resulting sur…

06:27

The given curve is rotated about the $y$ -axis. Find the area of the resulting …

02:11

Find the exact area of the surface obtained by rotating the curve about the x-a…
Additional Mathematics Questions

05:31

Prove that: sinA- cosA+1/ sinA + cosA -1 = 1/secA -tanA

01:03

Write the sun of 3x and 2y in algebraic expression

01:34

In a ΔABC, if ∟A = 50 degreeand ∟B = 60 degree, determine the shortest and t…

02:31

5 candidates apply of job interview, probability of selection is 1/2 eachWha…

01:36

what should be added to 10x^3 - 4x^2 + 10x to get 14x^3 + x^2-x

01:10

find the number of ways in which 8 different beads can be arranged to form a…

00:47

if f =20, V =12, and b =30 then verify Euler's formula

01:49

A bank returns 3000 as amount after 5years on the sum of 2000. Find therate …

05:20

a bag contains 3 red 5 black and another bag 2 red ,5 black two balls are dr…

02:23

the sum of two digit number is 9 if 27 subtracted from the number its digits…

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