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

Calculate the average value of $ f(x) = x \sec^2 …

03:46

Question

Answered step-by-step

Problem 65 Hard Difficulty

Calculate the volume generated by rotating the region bounded by the curves $ y = \ln x $, $ y = 0 $ and $ x = 2 $ about each axis.
(a) The y-axis
(b) The x-axis


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

WZ
Wen Zheng
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Wen Zheng

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 1

Integration by Parts

Related Topics

Integration Techniques

Discussion

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

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

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

03:07

Calculate the volume gener…

00:29

Find the volume generated …

02:41

Find the volume generated …

00:30

Find the volume generated …

00:37

Find the volume generated …

08:30

Find the volume obtained b…

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

Video Transcript

The problem is calculated: the volume generated by rotating the region, bounded by the curves y, equal to x y equal to 0 and x, equal to 2 about each axis, is about the y axis is about x axis, so first we can jarrah x and y, and It s there's a graph of the curve y go to x y equals to 0 and x equal to twont, so the region is this part now for a? If we retain this region about y axis, then we can use cylindrical shell method to find the volume is equal to 2 pi, integral from 1 to 2 x times x d x. Then we kind o use method of integration by powers that, u is equal to? U n x and the aprons equal to x, then you prom is equal to 1 over x and the v is equal to 1 half x squared. So this is equal to 2 pi times, u times 3. So this is 1 half x, squared x from 1 to 2 minus the integral from 1 to 2 on your prime times was so. This is 1 half like the x. This is equal to 2 pi times plunging 2 and 1 to this function. This is 2 times in 2, minus 0 and minus 1 fourth x, squared from 1 to 2 point. This is 2 pi times 2 times into minus. This is 3 over 4 foyotthis region about x axis. So we kind of use this kamis is equal to integral from 1 to 2 pi times n x square, then for this integral we can light, can also use integration by parts and that u is equal to x square and is equal to 1. Then your prime is equal to 2 times x, ove x and the prime and is equal to x pot. Now this integral is equal to pi times: u times 3. So this is x, l n x, squared from 1 to 2 minus integral from 1 to 2 priss 2 times x. Now, for this integral we can use integration by pontais equal to u n, x and apron is equal to 1 and prim is equal to 1. Over x and v is equal to x, so this is equal to pi times plug in 2 and 1 to this function. This is 2 into square. Minus 2 times is integration by parts, so this is x and x from 1 to 2 minus integral from 1 to 2. So this is equal to pi 2 times l into square minus 2 times 2 times. N 2 minus this is 1. This is the result.

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
83
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
52
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

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

03:07

Calculate the volume generated by rotating the region bounded by the following …

00:29

Find the volume generated by rotating about the $x$ -axis the regions bounded b…

02:41

Find the volume generated by rotating the area bounded by the graphs of each se…

00:30

Find the volume generated by rotating about the $x$ -axis the regions bounded b…

00:37

Find the volume generated by rotating about the $x$ -axis the regions bounded b…

08:30

Find the volume obtained by rotating the region bounded by the curves about the…
Additional Mathematics Questions

01:02

If the mass of a metal bar which is 3.25 m long is 15kg find its mass per un…

01:07

Find the cube root of 2197 by successive subtraction . Plz help

01:20

12. The edges of two solid metalic cube are 10 cm and 9 cm respectively. On …

01:15

if mean and mode of a data are respectively 24 and 12 then what is median of…

03:41

A man sold a fan for RS. 467. fine the cost price if he incurred a loss of 7…

00:57

Find the arithmetic mean of the following numbers -5, 12, 24, 46, 60

00:25

34 is ............. of the following number set 29 33 34 34 35

02:04

2.) On a shelf, the first row contains 25% more books than the second row, a…

02:18

2.1 Santosh swims 4/5 of a lap on Monday and2/5of a lap on Tuesday. On which…

00:43

The place value of 9 in the numeral 90521367 is ninety million?

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