/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 58 Consider the region between the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 58 (page 512)

Consider the region between the graph of fx=1-cosxand the x-axison 0,蟺. For the each line of rotation, write down definite integrals that represent the volume of the resulting solid and then use a calculator or computer to approximate the integrals.

Short Answer

Expert verified

The answer isV=蟺22-3蟺2鈮�24.674

Step by step solution

01

Step 1. Given information

Given the graph of fx=1-cosxand x-axison 0,蟺and the figure is

02

Step 2. Let us find the volume of solid.

The volume of solid of revolution Rxand rxrotated along x-axison interval a,bisrole="math" localid="1649522865857" V=蟺鈭�abRx2-rx2dx

Then, substitute the values

role="math" localid="1649523475727" V=蟺鈭�0蟺1-cosx2-22dxV=蟺鈭�0蟺1-cosx2-4dxV=蟺鈭�0蟺1-2cosx+cos2x-4dxV=蟺鈭�0蟺-2cosx+cos2x-3dxV=蟺鈭�0蟺-2cosxdx+鈭�0蟺cos2xdx-鈭�0蟺3dxV=蟺0+蟺2-3蟺V=蟺22-3蟺2鈮�24.674

The answer isV=蟺22-3蟺2鈮�24.674

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 exercise 13-18 decide which if either is larger without computing the integrals

蟺鈭�02x4dxand蟺鈭�02(x4-16)dx

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.

37.dydx=xy,y0=-1

Consider the region between f(x)=xand the x-axis on [0,4]. For each line of rotation given in Exercises 27鈥�30, use four disks or washers based on the given rectangles to approximate the volume of the resulting solid.

Solve the initial value problem

dydx=y2sinx,y蟺=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=4-x ,a,b=2,5
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.