BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Solutions

Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. Then use your calculator to find the surface area correct to four decimal places.

60. x = t2t3, y = t + t4, 0 ≤ t ≤ 1

To determine

To find: The surface area of the curve for the parametric equation x=t2t3 and y=t+t4.

Explanation

Given:

The parametric equation for the variable x is x=t2t3.

The parametric equation for the variable y is y=t+t4.

The value t ranges from 0 to 1.

Calculation:

The surface area of the surface obtained by rotating curve about the x axis S=012πy(dxdt)2+(dydt)2dt.

The value t ranges from 0 to 1.

Differentiate the variable x with respect to t.

x=t2t3dxdt=3t3t2

Differentiate the variable y with respect to t:

y=tt4dxdt=14t3

Write the surface area formula.

S=132πy(dxdt)2+(dydt)2dt

Substitute (3t3t2) for dxdt and (14t3) for dydt in the above equation

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 10 Solutions

Show all chapter solutions add
Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 P-25ESect-10.2 P-26ESect-10.2 P-27ESect-10.2 P-28ESect-10.2 P-29ESect-10.2 P-30ESect-10.2 P-31ESect-10.2 P-32ESect-10.2 P-33ESect-10.2 P-34ESect-10.2 P-35ESect-10.2 P-36ESect-10.2 P-37ESect-10.2 P-38ESect-10.2 P-39ESect-10.2 P-40ESect-10.2 P-41ESect-10.2 P-42ESect-10.2 P-43ESect-10.2 P-44ESect-10.2 P-45ESect-10.2 P-46ESect-10.2 P-47ESect-10.2 P-48ESect-10.2 P-49ESect-10.2 P-50ESect-10.2 P-51ESect-10.2 P-52ESect-10.2 P-53ESect-10.2 P-54ESect-10.2 P-55ESect-10.2 P-57ESect-10.2 P-58ESect-10.2 P-59ESect-10.2 P-60ESect-10.2 P-61ESect-10.2 P-62ESect-10.2 P-63ESect-10.2 P-64ESect-10.2 P-65ESect-10.2 P-66ESect-10.2 P-67ESect-10.2 P-68ESect-10.2 P-69ESect-10.2 P-70ESect-10.2 P-71ESect-10.2 P-72ESect-10.2 P-73ESect-10.2 P-74ESect-10.3 P-1ESect-10.3 P-2ESect-10.3 P-3ESect-10.3 P-4ESect-10.3 P-5ESect-10.3 P-6ESect-10.3 P-7ESect-10.3 P-8ESect-10.3 P-9ESect-10.3 P-10ESect-10.3 P-11ESect-10.3 P-12ESect-10.3 P-13ESect-10.3 P-14ESect-10.3 P-15ESect-10.3 P-16ESect-10.3 P-17ESect-10.3 P-18ESect-10.3 P-19ESect-10.3 P-20ESect-10.3 P-21ESect-10.3 P-22ESect-10.3 P-23ESect-10.3 P-24ESect-10.3 P-25ESect-10.3 P-26ESect-10.3 P-27ESect-10.3 P-28ESect-10.3 P-29ESect-10.3 P-30ESect-10.3 P-31ESect-10.3 P-32ESect-10.3 P-33ESect-10.3 P-34ESect-10.3 P-35ESect-10.3 P-36ESect-10.3 P-37ESect-10.3 P-38ESect-10.3 P-39ESect-10.3 P-40ESect-10.3 P-41ESect-10.3 P-42ESect-10.3 P-43ESect-10.3 P-44ESect-10.3 P-45ESect-10.3 P-46ESect-10.3 P-47ESect-10.3 P-48ESect-10.3 P-49ESect-10.3 P-50ESect-10.3 P-51ESect-10.3 P-52ESect-10.3 P-53ESect-10.3 P-54ESect-10.3 P-55ESect-10.3 P-56ESect-10.3 P-57ESect-10.3 P-58ESect-10.3 P-59ESect-10.3 P-60ESect-10.3 P-61ESect-10.3 P-62ESect-10.3 P-63ESect-10.3 P-64ESect-10.3 P-65ESect-10.3 P-66ESect-10.3 P-67ESect-10.3 P-68ESect-10.3 P-69ESect-10.3 P-70ESect-10.3 P-71ESect-10.3 P-72ESect-10.3 P-73ESect-10.3 P-74ESect-10.3 P-75ESect-10.3 P-76ESect-10.3 P-77ESect-10.3 P-78ESect-10.4 P-1ESect-10.4 P-2ESect-10.4 P-3ESect-10.4 P-4ESect-10.4 P-5ESect-10.4 P-6ESect-10.4 P-7ESect-10.4 P-8ESect-10.4 P-9ESect-10.4 P-10ESect-10.4 P-11ESect-10.4 P-12ESect-10.4 P-13ESect-10.4 P-14ESect-10.4 P-15ESect-10.4 P-16ESect-10.4 P-17ESect-10.4 P-18ESect-10.4 P-19ESect-10.4 P-20ESect-10.4 P-21ESect-10.4 P-22ESect-10.4 P-23ESect-10.4 P-24ESect-10.4 P-25ESect-10.4 P-26ESect-10.4 P-27ESect-10.4 P-28ESect-10.4 P-29ESect-10.4 P-30ESect-10.4 P-31ESect-10.4 P-32ESect-10.4 P-33ESect-10.4 P-34ESect-10.4 P-35ESect-10.4 P-36ESect-10.4 P-37ESect-10.4 P-38ESect-10.4 P-39ESect-10.4 P-40ESect-10.4 P-41ESect-10.4 P-42ESect-10.4 P-43ESect-10.4 P-44ESect-10.4 P-45ESect-10.4 P-46ESect-10.4 P-47ESect-10.4 P-48ESect-10.4 P-49ESect-10.4 P-50ESect-10.4 P-51ESect-10.4 P-52ESect-10.4 P-53ESect-10.4 P-54ESect-10.4 P-55ESect-10.4 P-56ESect-10.5 P-1ESect-10.5 P-2ESect-10.5 P-3ESect-10.5 P-4ESect-10.5 P-5ESect-10.5 P-6ESect-10.5 P-7ESect-10.5 P-8ESect-10.5 P-9ESect-10.5 P-10ESect-10.5 P-11ESect-10.5 P-12ESect-10.5 P-13ESect-10.5 P-14ESect-10.5 P-15ESect-10.5 P-16ESect-10.5 P-17ESect-10.5 P-18ESect-10.5 P-19ESect-10.5 P-20ESect-10.5 P-21ESect-10.5 P-22ESect-10.5 P-23ESect-10.5 P-24ESect-10.5 P-25ESect-10.5 P-26ESect-10.5 P-27ESect-10.5 P-28ESect-10.5 P-29ESect-10.5 P-30ESect-10.5 P-31ESect-10.5 P-32ESect-10.5 P-33ESect-10.5 P-34ESect-10.5 P-35ESect-10.5 P-36ESect-10.5 P-37ESect-10.5 P-38ESect-10.5 P-39ESect-10.5 P-40ESect-10.5 P-41ESect-10.5 P-42ESect-10.5 P-43ESect-10.5 P-44ESect-10.5 P-45ESect-10.5 P-46ESect-10.5 P-47ESect-10.5 P-48ESect-10.5 P-49ESect-10.5 P-50ESect-10.5 P-51ESect-10.5 P-52ESect-10.5 P-53ESect-10.5 P-54ESect-10.5 P-55ESect-10.5 P-56ESect-10.5 P-57ESect-10.5 P-58ESect-10.5 P-59ESect-10.5 P-60ESect-10.5 P-61ESect-10.5 P-62ESect-10.5 P-63ESect-10.5 P-64ESect-10.5 P-65ESect-10.5 P-66ESect-10.6 P-1ESect-10.6 P-2ESect-10.6 P-3ESect-10.6 P-4ESect-10.6 P-5ESect-10.6 P-6ESect-10.6 P-7ESect-10.6 P-8ESect-10.6 P-9ESect-10.6 P-10ESect-10.6 P-11ESect-10.6 P-12ESect-10.6 P-13ESect-10.6 P-14ESect-10.6 P-15ESect-10.6 P-16ESect-10.6 P-17ESect-10.6 P-18ESect-10.6 P-19ESect-10.6 P-20ESect-10.6 P-21ESect-10.6 P-22ESect-10.6 P-23ESect-10.6 P-24ESect-10.6 P-25ESect-10.6 P-26ESect-10.6 P-27ESect-10.6 P-28ESect-10.6 P-29ESect-10.6 P-30ESect-10.6 P-31ECh-10 P-1RCCCh-10 P-2RCCCh-10 P-3RCCCh-10 P-4RCCCh-10 P-5RCCCh-10 P-6RCCCh-10 P-7RCCCh-10 P-8RCCCh-10 P-9RCCCh-10 P-1RQCh-10 P-2RQCh-10 P-3RQCh-10 P-4RQCh-10 P-5RQCh-10 P-6RQCh-10 P-7RQCh-10 P-8RQCh-10 P-9RQCh-10 P-10RQCh-10 P-1RECh-10 P-2RECh-10 P-3RECh-10 P-4RECh-10 P-5RECh-10 P-6RECh-10 P-7RECh-10 P-8RECh-10 P-9RECh-10 P-10RECh-10 P-11RECh-10 P-12RECh-10 P-13RECh-10 P-14RECh-10 P-15RECh-10 P-16RECh-10 P-17RECh-10 P-18RECh-10 P-19RECh-10 P-20RECh-10 P-21RECh-10 P-22RECh-10 P-23RECh-10 P-24RECh-10 P-25RECh-10 P-26RECh-10 P-27RECh-10 P-28RECh-10 P-29RECh-10 P-30RECh-10 P-31RECh-10 P-32RECh-10 P-33RECh-10 P-34RECh-10 P-35RECh-10 P-36RECh-10 P-37RECh-10 P-38RECh-10 P-39RECh-10 P-40RECh-10 P-41RECh-10 P-42RECh-10 P-43RECh-10 P-44RECh-10 P-45RECh-10 P-46RECh-10 P-47RECh-10 P-48RECh-10 P-49RECh-10 P-50RECh-10 P-51RECh-10 P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Find the maximum revenue R (in dollars) given that 12(2R 320) 4(3R + 240)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Simplify: 66

Elementary Technical Mathematics

Using as an estimator, find the maximum error in estimating with the Midpoint Rule and 8 subintervals. 9

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Why are studies that examine the effects of aging not considered true experiments?

Research Methods for the Behavioral Sciences (MindTap Course List)