Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 26 (page 510)

Write the volume of the two solids of revolution that follow in terms of definite integrals that represent accumulations of disks and/or washers. Do not compute the integrals.

Short Answer

Expert verified

The required volume isπ∫03(fx)2-12dx

Step by step solution

01

Step 1. Given Information  

The given figure is

02

Step 2. Explanation    

A solid of revolution is being formed by rotating the region around x-axis.

The given figure can be shown as below,

The part of region above x-axis is not bounded by x-axis. But it can be expressed as a washer with outer radius being the graph of the function and inner radius is the graph of y=1. The x-interval for this region is 0,4

Thus, the integral of the volume of solid formed by rotating the given region is expressed as π∫03(fx)2-12dx

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

For each pair of definite integrals in Exercises 13–18, decide which, if either, is larger, without computing any integrals.

π∫04ydyandπ∫48(8-y)dy

dydx=5y,y0=1

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=3x+1,a,b=-1,4

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.

Consider the region between the graph of f(x)=x-2and the x-axis on [2,5]. For each line of rotation given in Exercises 35– 40, use definite integrals to find the volume of the resulting solid.

See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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