Use both the Shell and Disk Methods to calculate the volume of the solid obtained by rotating the region under the graph of f(x) = 2x³ for 0≤x≤ 2 about the x-axis and the y-axis. Using the disk method, the volume D₂ of the solid obtained by rotating the region about the x-axis is fog(x) dx (this is the initial integral when you setup the problem), where a = g(x)= D₂= Using the shell method, the volume S₂ of the solid obtained by rotating the region about the x-axis is foh(y)dy (this is the initial integral when you setup the problem), where b= h(y)= S₂= Using the disk method, the volume Dy of the solid obtained by rotating the region about the y-axis is G(y)dy (this is the initial integral when you setup the problem), where A = G(y)= Dy= Using the shell method, the volume Sy of the solid obtained by rotating the region about the y-axis is H(x)dx (this is the initial integral when you setup the problem), where B= H(x)= Sy=
Use both the Shell and Disk Methods to calculate the volume of the solid obtained by rotating the region under the graph of f(x) = 2x³ for 0≤x≤ 2 about the x-axis and the y-axis. Using the disk method, the volume D₂ of the solid obtained by rotating the region about the x-axis is fog(x) dx (this is the initial integral when you setup the problem), where a = g(x)= D₂= Using the shell method, the volume S₂ of the solid obtained by rotating the region about the x-axis is foh(y)dy (this is the initial integral when you setup the problem), where b= h(y)= S₂= Using the disk method, the volume Dy of the solid obtained by rotating the region about the y-axis is G(y)dy (this is the initial integral when you setup the problem), where A = G(y)= Dy= Using the shell method, the volume Sy of the solid obtained by rotating the region about the y-axis is H(x)dx (this is the initial integral when you setup the problem), where B= H(x)= Sy=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use both the Shell and Disk Methods to calculate the volume of the solid obtained by rotating the region under the graph of f(x) = 2 − x³ for 0 ≤ x ≤ 2} about the x-axis and
the y-axis.
Using the disk method, the volume D, of the solid obtained by rotating the region about the x-axis is ſº g(x) dx (this is the initial integral when you setup the problem), where
a =
g(x)=
Dx=
Using the shell method, the volume S of the solid obtained by rotating the region about the x-axis is ſh(y)dy (this is the initial integral when you setup the problem), where
b=
h(y)=
Sx=
Using the disk method, the volume Dy of the solid obtained by rotating the region about the y-axis is SG(y)dy (this is the initial integral when you setup the problem), where
A =
G(y)=
D₂=
Using the shell method, the volume Sy of the solid obtained by rotating the region about the y-axis is ³ H(x) dx (this is the initial integral when you setup the problem), where
B=
H(x)=
S₂=
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