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Let R be the region in the lower half of the circle of radius 2 centred at (x, y) = (2,6). The volume of the solid obtained by rotating R about the line y = -4 is given by V T --foo

Let R be the region in the lower half of the circle of radius 2 centred at (x, y) = (2,6). The volume of the solid obtained by rotating R about the line y = -4 is given by V T --foo

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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Let R be the region in the lower half of the circle of radius 2 centred at (x, y) = (2,6). The volume of the solid obtained by rotating R about the line y = -4 is given by V = T -Poo
Transcribed Image Text:Let R be the region in the lower half of the circle of radius 2 centred at (x, y) = (2,6). The volume of the solid obtained by rotating R about the line y = -4 is given by V = T -Poo
Expert Solution
Step 1: Finding the values

The equation of the circle whose center at 2,6 and radius 2 is x-22+y-62=4

Advanced Math homework question answer, step 1, image 1

The lower half of the circle is rotated about y=-4

Applying Cylindrical shell method

Advanced Math homework question answer, step 1, image 2

V=∫ab2πxfxdxfx=4+6-4-x-22       =10-4-x-22

The limit of the integration is x=0 →x=4

 

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