Question

How do I find the Volume of the Solid of revolution generated by revolving the region bounded by the graphs of the given equations about the indicated line.
y= 1/x, y=0, x=1, x=0; about the line y=6

Answer 1

I suspect a typo. The given region is unbounded. x=0 is an asymptote.

Answer 2

oh jeez yeah it is x=4

Answer 3

there is a typo, these are the equations:
y=1/x, y=0, x=1, x=4; about y=6

Answer 4

That's better.
Using discs of thickness dx,
v = ∫[1,4] π(R^2-r^2) dx
where R=6 and r = 6-y
Thus,
v = ∫[1,4] π(6^2 - (6 - 1/x)^2) dx

Answer 5

Thank you!