Asked by Jessica
Let R be the region bounded by y = ln x, x-axis, and x = 3. Answer the following.
a) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about x = -2.
b) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about y = 4.
I am confused about this question as well. Could you please help me understand how to do this? I would greatly appreciate it!
a) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about x = -2.
b) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about y = 4.
I am confused about this question as well. Could you please help me understand how to do this? I would greatly appreciate it!
Answers
Answered by
Steve
(a) using shells,
v = ∫[1,3] 2πrh dx
where r = x+2 and h=y=ln(x)
using discs,
v = ∫[0,ln3] π(R^2-r^2) dy
where R=5 and r=x+2=2+e^y
(b) use the same ideas with a horizontal axis. Just keep in mind the volume of a disc (or a washer with a hole inside) and a cylinder. I usually try to do it both ways to make sure the answers agree.
v = ∫[1,3] 2πrh dx
where r = x+2 and h=y=ln(x)
using discs,
v = ∫[0,ln3] π(R^2-r^2) dy
where R=5 and r=x+2=2+e^y
(b) use the same ideas with a horizontal axis. Just keep in mind the volume of a disc (or a washer with a hole inside) and a cylinder. I usually try to do it both ways to make sure the answers agree.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.