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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 5.3, Problem 11E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

y = x 3 / 2 ,    y = 8 ,    x = 0

To determine

To find:

The volume generated by rotating the region bounded by the given curves about the x-axis using the cylindrical shells.

Explanation

1) Concept:

i. If y  is the radius of the typical shell, then the circumference =2πy .

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

V= ∫ab2πyf(y)dy

where  0≤a≤b

2) Given:

The region bounded by y=x32, x=0, y=8 rotated about the x- axis.

3) Calculation:

As the region is bounded by

y=x32 ⇒x=y23, x=0, y=8

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

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Chapter 5.3,
Problem 10E
Chapter 5.3,
Problem 12E
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