Explanation 1) Concept: i. If the cross section is a disc and the radius of the disc is in terms of x or y then area A = π r a d i u s 2 ii. The volume of a solid revolution about the x -axis is V = ∫ a b A ( x ) d x 2) Given: y = tan ⁡ x , y = 0 , x = π 4 , a b o u t t h e x - a x i s 3) Calculation: Bounded region of the given curves is as shown below: From the above graph The solid lies between x = 0 and x = π 4 The region rotates about the x - a x i s , so the cross-section is perpendicular to the To determine Part (b): i. To set up: An integral for the volume of solid obtained by rotating the region bounded by the given curves about the line y = - 1 . ii. To evaluate : The integral by using the calculator up to five decimal places

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ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.2, Problem 31E

To determine

Part (a):

i. To set up:

An integral for the volume of solid obtained by rotating the region bounded by the given curves about the x axis.

ii. $2:

The integral by using the calculator up to five decimal places.

To determine

Part (b):

i. To set up:

An integral for the volume of solid obtained by rotating the region bounded by the given curves about the line y= -1.

ii. To evaluate:

The integral by using the calculator up to five decimal places

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Chapter 5.2, Problem 30E

Chapter 5.2, Problem 32E

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Chapter 5 Solutions

Calculus (MindTap Course List)

Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Prob. 3E Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 10E

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Part (a): i. To set up: An integral for the volume of solid obtained by rotating the region bounded by the given curves about the x a x i s . ii. $2 : The integral by using the calculator up to five decimal places.

Solution Summary: The author explains how to set up an integral for the volume of solid obtained by rotating the region bounded by the given curves about the xaxis.

Videos

Part (a):

i. To set up:

An integral for the volume of solid obtained by rotating the region bounded by the given curves about the x axis.

ii. $2:

The integral by using the calculator up to five decimal places.

Part (b):

i. To set up:

An integral for the volume of solid obtained by rotating the region bounded by the given curves about the line y= -1.

ii. To evaluate:

The integral by using the calculator up to five decimal places

Want to see the full answer?

Chapter 5 Solutions

Part (a): i. To set up: An integral for the volume of solid obtained by rotating the region bounded by the given curves about the x a x i s . ii. $2 : The integral by using the calculator up to five decimal places.

Solution Summary: The author explains how to set up an integral for the volume of solid obtained by rotating the region bounded by the given curves about the xaxis.

Videos

Part (a): i. To set up: An integral for the volume of solid obtained by rotating the region bounded by the given curves about the x axis. ii. $2: The integral by using the calculator up to five decimal places.

Part (b): i. To set up: An integral for the volume of solid obtained by rotating the region bounded by the given curves about the line y= -1. ii. To evaluate: The integral by using the calculator up to five decimal places

Want to see the full answer?

Chapter 5 Solutions

Part (a):

i. To set up:

An integral for the volume of solid obtained by rotating the region bounded by the given curves about the x axis.

ii. $2:

The integral by using the calculator up to five decimal places.

Part (b):

i. To set up:

An integral for the volume of solid obtained by rotating the region bounded by the given curves about the line y= -1.

ii. To evaluate:

The integral by using the calculator up to five decimal places