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

(a) Set up an integral for the area of the surfac…

06:14

Question

Answered step-by-step

Problem 1 Easy Difficulty

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x-axis and (ii) the y-axis.
(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.

$ y = \tan x $ , $ 0 \le x \le \frac{\pi}{3} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Carlos Pinilla
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Carlos Pinilla

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.
SK

Saira K.

October 17, 2021

integration

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

03:34

(a) Set up an integral for…

06:05

(a) Set up an integral for…

02:29

(a) Set up an integral for…

07:06

(a) Set up an integral for…

10:13

(a) Set up an integral for…

06:14

(a) Set up an integral for…

04:47

(a) Set up an integral for…

06:51

(a) Set up an integral for…

13:12

(a) Set up an integral for…

02:56

(a) Set up an integral for…

07:27

(a) Set up an integral for…

0:00

Set up an integral for 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

the following problem. You have, uh, of this curved? Yeah, in the x y plane. Because he's, uh why is he going to tangent Effects? Is this Why equals tangent off X way? Have that curve from X equals to zero up to, um what is yours Aware? Uh, Kennedy at my house. Somebody we have these one up to thirds. And so all this continues here. So you have to consider just this portion from zero of two by thirds When you want to do the following First of all this money, want to update about the the X axis? Correct. Would rotate that piece. This piece from zero up to buy thirds off. I didn't like that. You get something like that, Someone sort of like a trumpet. Something like that. So I want to compute. What is the area of this? Um, so with the x axis and then Well, look, we also like to rotate about the y axis. So you have the that curve here is the Y axis. This is our nice, wonderful curve on the Reato. Look, take on there. So we're gonna obtained, like, a a bowl, something like that. Were they so not to compute the area of these two services for this one. You know that, uh, by formula or the it's gonna be being to go from zero up to buy thirds. So after five thirds Yeah, off from, uh, if effects, uh is, um, all the length of the curve? Uh, just yes. Which of these The length of this car would be? School one. Bless crime squared. Well, that dance by. So that is the formula on the wall for this rotation about the X axis. And also this is that would be why this part here is why on then we rotate all the the X axis are what changes here. Is that here? Yeah, they dropped by from here. The bikers, uh, deep items. What appears here's would be just X consents. The X, um so for dysfunction for effects being called toe tangent fax over dessert. If effects of crime is equal to Seacon square, the roofs tangent this second so that, uh, over this thing to go Well, let's call these ones. Uh, mhm. So that is gonna be equal to yeah. To buy is two pi times the intro from zero up to by thirds off or function pungent fakes. Clams s. So these would be square root of one plus this square. So see, Camp Squared Square would be just speak into the fourth. See that square affects. Oh, that square is ableto see them to the fourth power. So you have seeking to the fourth? Yeah, it's the fourth is the X. So that is our first one we're taking about about X from being If you're a date about why do you have this? So that sort of it is, uh is she called to seven? One will be to fight. There was interest from 0 to 5 thirds. It affects Champs Square it off all the same. One last sentence. Uh, the fourth power that effects the fourth power. Yes. Way opposed to approximate that with our favorite calculator. Um, this is, um, 10 point 517 from this is seven 0.9 35 Okay, so those are the the approximation studies areas of revolution like that. Like that? Wow.

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
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Recommended Videos

03:34

(a) Set up an integral for the area of the surface obtained by rotating the cur…

06:05

(a) Set up an integral for the area of the surface obtained by rotating the cur…

02:29

(a) Set up an integral for the area of the surface obtained by rotating the cur…

07:06

(a) Set up an integral for the area of the surface obtained by rotating the cur…

10:13

(a) Set up an integral for the area of the surface obtained by rotating the cur…

06:14

(a) Set up an integral for the area of the surface obtained by rotating the cur…

04:47

(a) Set up an integral for the area of the surface obtained by rotating the cur…

06:51

(a) Set up an integral for the area of the surface obtained by rotating the cur…

13:12

(a) Set up an integral for the area of the surface obtained by rotating the cur…

02:56

(a) Set up an integral for the area of the surface obtained by rotating the cur…

07:27

(a) Set up an integral for the area of the surface obtained by rotating the cur…

0:00

Set up an integral for the area of the surface obtained by rotating the given c…

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