BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y = tan x ,   y = x ,   x = π / 3 ; about the y -axis

To determine

To set up:

An integral for the volume of a solid.

Explanation

1) Concept:

If x  is the radius of a typical shell, then circumference=2πx and height is y=f(x).

By shell method, the volume of the solid obtained by rotating the region under the curve y=f(x) from a to b about y- axis is

V= ab2πxf(x)dx;axb

where 2πx  is circumference, fx is height, and dx  is the thickness of the shell.

2) Given:

y=tanx,y=x,x= π3;

about the y  axis.

3) Calculation:

The equation of given curves is

y=tanx, y=x

The region and typical shell are shown in the figure.

The graph shows the region and height of cylindrical shell formed by rotation about the y-axis.

It has radius =x

Using shell method, find the typical approximating shell with radius  x

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
Sect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.1 P-42ESect-5.1 P-43ESect-5.1 P-44ESect-5.1 P-45ESect-5.1 P-46ESect-5.1 P-47ESect-5.1 P-48ESect-5.1 P-49ESect-5.1 P-50ESect-5.1 P-51ESect-5.1 P-52ESect-5.1 P-53ESect-5.1 P-54ESect-5.1 P-55ESect-5.1 P-56ESect-5.1 P-57ESect-5.1 P-58ESect-5.1 P-59ESect-5.1 P-60ESect-5.1 P-61ESect-5.1 P-62ESect-5.1 P-63ESect-5.1 P-64ESect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-13ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-31ESect-5.2 P-32ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.2 P-63ESect-5.2 P-64ESect-5.2 P-65ESect-5.2 P-66ESect-5.2 P-67ESect-5.2 P-68ESect-5.2 P-69ESect-5.2 P-70ESect-5.2 P-71ESect-5.2 P-72ESect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.R P-1CCSect-5.R P-2CCSect-5.R P-3CCSect-5.R P-4CCSect-5.R P-5CCSect-5.R P-6CCSect-5.R P-1ESect-5.R P-2ESect-5.R P-3ESect-5.R P-4ESect-5.R P-5ESect-5.R P-6ESect-5.R P-7ESect-5.R P-8ESect-5.R P-9ESect-5.R P-10ESect-5.R P-11ESect-5.R P-12ESect-5.R P-13ESect-5.R P-14ESect-5.R P-15ESect-5.R P-16ESect-5.R P-17ESect-5.R P-18ESect-5.R P-19ESect-5.R P-20ESect-5.R P-21ESect-5.R P-22ESect-5.R P-23ESect-5.R P-24ESect-5.R P-25ESect-5.R P-26ESect-5.R P-27ESect-5.R P-28ESect-5.R P-29ESect-5.R P-30ESect-5.R P-31ESect-5.R P-32ESect-5.R P-33ESect-5.R P-34ESect-5.P P-1PSect-5.P P-2PSect-5.P P-3PSect-5.P P-4PSect-5.P P-5PSect-5.P P-6PSect-5.P P-7PSect-5.P P-8PSect-5.P P-9PSect-5.P P-10PSect-5.P P-11PSect-5.P P-12PSect-5.P P-13PSect-5.P P-14PSect-5.P P-15P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 4449, find an equation of the line L that passes through the point (2, 4) and satisfies the condit...

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

For and

Study Guide for Stewart's Multivariable Calculus, 8th

For f(x) = x3 + 7x, df = _____. a) (x3 + 7x) dx b) (3x2 + 7) dx c) 3x2 + 7 d) x3 + 7x + dx

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

Find gage dimension y. All dimensions are in inches

Mathematics For Machine Technology

Explain how the mean and the standard deviation describe a distribution of scores.

Research Methods for the Behavioral Sciences (MindTap Course List)