Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 20 (page 522)

Write the volumes of the solids of revolution shown in Exercises 17–20 in terms of definite integrals that represent accumulations of shells. Do not solve the integrals.

Short Answer

Expert verified

The volume of the solid in terms of definite integral is 2π∫12y1-f-1ydy.

Step by step solution

01

Step 1. Given information.

Consider the given figure that represent accumulations of shells.

02

Step 2. Find the volume of solid in terms of definite integral. 

The function is terms of y is:

y=fxx=f-1x

From y=1to y=2, the height of the shell at yk*will be the difference role="math" localid="1649337266897" 1-yk*.

So, the volume of the solid obtained by revolving the function about the x-axis shown in the figure is:

V=2π∫12y1-f-1ydy

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral .

fx=x32,a,b=0,2

Sketching a representative disks ,washers and shells : sketch a representative disks , washers , shells for the solid obtained by revolving the regions shown in figure around the given lines .

The x axis

Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral .

fx=2x32+1,1,3

Consider the region between the graph of f(x)=3xand the x-axis on [1,3]. For each line of rotation given in Exercises 31– 34, use definite integrals to find the volume of the resulting solid.

Each of the definite integrals in Exercises 19–24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.

π∫13(x2-2x+1)dx
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free