1. Area of R = [(ln x) – (x-2)] dx
Part (a)
Area of R = [(ln x) – (x-2)] dx
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Area of R = units2
The intersection points can be found using the graphing calculator. They are x= and x=

2. Volume of R = p [(ln(x) +3)2 – (x-2 +3)2] dx
Part (b)
Volume of R = p [(ln(x) +3)2 – (x-2 +3)2] dx
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Volume of R = p [(ln(x)+3)2 – (x+1)2] dx
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(x, ln x)
(x, x-2) 3
y = -3
Volume of R = or units3

3. shell method Part (c) Volume of R = 2p x [(ln x) – (x-2)] dx ???
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shell method