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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
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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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
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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