Consider the curve y = 1 for x > 1. (a) Determine the volume created by revolving the area under this curve and above the x-axis around the x-axis. This means setup and evaluate an integral for the volume. (b) Show using Comparison Test that the surface area of the shape created by revolving this curve around the x-axis diverges to infinity.
Consider the curve y = 1 for x > 1. (a) Determine the volume created by revolving the area under this curve and above the x-axis around the x-axis. This means setup and evaluate an integral for the volume. (b) Show using Comparison Test that the surface area of the shape created by revolving this curve around the x-axis diverges to infinity.
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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I just need this checked and corrected please
Transcribed Image Text:In this question you'll investigate an infinite 3D shape known as Gabriel's Horn.
This shape strangely enough has a FINITE volume but an INFINITE surface area.
Consider the curve y = 1 for x > 1.
(a) Determine the volume created by revolving the area under this curve and above the x-axis
around the x-axis. This means setup and evaluate an integral for the volume.
(b) Show using Comparison Test that the surface area of the shape created by revolving this
curve around the x-axis diverges to infinity.
1/4 for x21.
x
x=( y=(
X=27=2
x= 1/2 y=2
P
* dx
(✗
Tim
red area
nt
Tim
+ dx
=
=
11
1
Tim
to in 1x1 / 2
Tim Intl - Inl1
+700
I'm In It! ∞ infinite area
+700
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