Explanation 1) Concept: Let S be a solid that lies between x = a and x = b . If the cross sectional area of S in the plane P x , through x and perpendicular to the x - a x i s , is A ( x ) , where A is continuous function, then the volume of S is V = lim n → ∞ ⁡ ∑ i = 1 n A x i * ∆ x = ∫ a b A x d x 2) Given: The equations of the curves are y = x & y = x 2 . 3) Calculation: The equations of curves are y = x & y = x 2 Draw the curves about x axis. The curves y = x & y = x 2 intersect at the points 0,0 & 1,1 . The region between them is the solid of rotation and across section perpendicular to x axis. The cross section in plane P x has the shape of a washer with the inner radius y = x 2 and outer radius y = x . So, find the cross sectional area by subtracting the area of the outer circle from the area of the inner circle, i.e To determine b) To find: The volume of a solid rotating the region about y - axis To determine c) To find: The volume of the solid rotating the region about y = 2 .

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.R, Problem 15E

To determine

a)

To find:

The volume of the solid rotating the region about x- axis

To determine

b)

To find:

The volume of a solid rotating the region about y- axis

To determine

c)

To find:

The volume of the solid rotating the region about y=2.

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Chapter 5.R, Problem 14E

Chapter 5.R, Problem 16E

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Chapter 5 Solutions

Calculus (MindTap Course List)

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a) To find: The volume of the solid rotating the region about x - axis

Solution Summary: The author explains how to find the volume of the solid rotating the region about x- axis.

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a)

To find:

The volume of the solid rotating the region about x- axis

b)

To find:

The volume of a solid rotating the region about y- axis

c)

To find:

The volume of the solid rotating the region about y=2.

Want to see the full answer?

Chapter 5 Solutions

a) To find: The volume of the solid rotating the region about x - axis

Solution Summary: The author explains how to find the volume of the solid rotating the region about x- axis.

Concept explainers

Videos

a) To find: The volume of the solid rotating the region about x- axis

b) To find: The volume of a solid rotating the region about y- axis

c) To find: The volume of the solid rotating the region about y=2.

Want to see the full answer?

Chapter 5 Solutions

a)

To find:

The volume of the solid rotating the region about x- axis

b)

To find:

The volume of a solid rotating the region about y- axis

c)

To find:

The volume of the solid rotating the region about y=2.