Question

solid of revolution.

y=2
y=lnx

rotate around x=-1 and again around y=2

I know what the graph looks like. but am having trouble deciding on washer or shell method and how to apply them. i think shell might be easier but do not know how to set it up. for x=-1 would the radius be x+1 and height be 2-lnx ?? and am not sure on rotating around y=2

Answer 1

What do you mean by rotating about one line and again by another? Are these two separate solids, or are we "revolving a solid" about the second line?

Answer 2

yes two separate problems

Answer 3

one problem is around x=-1
the other is around y=2

Answer 4

they intersect at e^2 on the x-axis (if i am thinking correctly) but still dont know how to use that information. I can kind of fidure out points and stuff but have not quite figured out how to use that to solve the problem

Answer 5

what i mean by that is when it is not around an axis it is harder for me to figure out what to do

Answer 6

Alright, just to be sure, is the region bounded by anything else, or is it as drawn below?

Basically, are we also considering the area below the x-axis?