2) Region R, that is bounded by the graph y = 2+ Vx x=1 and y=2, is revolved about the line x=1 to form a solid of revolution. Answer the following questions: a) Sketch the region R b) What is the shape of the cross-section? c) Determine the direction/orientation of the cross- sections and then determine whether we are using dx or dy for the thickness. d) What is the general formula for the area of the cross- section? e) What is the expression of the area of the cross-section in terms of x and/or y? f) Set up the integral to calculate the volume of the solid. (Do not need to evaluate the integral)
2) Region R, that is bounded by the graph y = 2+ Vx x=1 and y=2, is revolved about the line x=1 to form a solid of revolution. Answer the following questions: a) Sketch the region R b) What is the shape of the cross-section? c) Determine the direction/orientation of the cross- sections and then determine whether we are using dx or dy for the thickness. d) What is the general formula for the area of the cross- section? e) What is the expression of the area of the cross-section in terms of x and/or y? f) Set up the integral to calculate the volume of the solid. (Do not need to evaluate the integral)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For this section, the main idea is to set up the volume of a slice/cross-section as a cylinder whose volume can be calculated by the formula (area of cross-section)*(thickness). Thickness can be expressed as dx or dy depending on the orientation of the solid. The key step is to set up the area of the cross-section.
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Transcribed Image Text:2) Region R, that is bounded by the graph Y = 2+ Vx
X=1 and y=2, is revolved about the line x=1 to form a solid of
revolution. Answer the following questions:
a) Sketch the region R
b) What is the shape of the cross-section?
c) Determine the direction/orientation of the cross-
sections and then determine whether we are using dx or dy
for the thickness.
d) What is the general formula for the area of the cross-
section?
e) What is the expression of the area of the cross-section
in terms of x and/or y?
f) Set up the integral to calculate the volume of the solid.
(Do not need to evaluate the integral)
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