Maths Volume Integration question (1 Viewer)

flowerp

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Hi everyone, I would like help with the following question from Cambridge Yr 11 Ex 12E please:
Find the volume of the rotation of the area in the first quadrant under y = 1 and above y = 2 - 2/x about the x-axis.

Thank you sooooo much!!
 
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Drongoski

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The area above the x-axis between y = 1 and y = 2 - 2/x can be split into 2 parts, A and B
The latter curve cuts the x-axis at x=1, and the line y=1 at x=2. Rotating about the x-axis, A generates the volume of a cylinder (height 1, radius 1) = .
B generates:




This is my 1st solution post in half a year, after having trouble logging on previously!
 
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flowerp

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The area above the x-axis between y = 1 and y = 2 - 2/x can be split into 2 parts, A and B
The latter curve cuts the x-axis at x=1, and the line y=1 at x=2. Rotating about the x-axis, A generates the volume of a cylinder (height 1, radius 1) = .
B generates:




This is my 1st solution post in half a year, after having trouble logging on previously!
Thank you soooo much for your assistance !!!!! Much appreciated :)
 

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