Uncertain about volume of bounded region question

[warfreak131]

Homework Statement

The question states:

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

The lines are, y=lnX, y = 1, y = 2, and x = 0, rotated about the y-axis.

I know how to integrate it, I just don't exactly know which region I'm taking the volume of, so I am having trouble setting up the integration problem.

I have provided a graph of the curves.

http://img691.imageshack.us/img691/2071/boundregion.png

EDIT:

I think I got it, here's my attempt at the solution:

I'm going to use the area of circles method going vertical. So I find the distance from the y-axis to the lnX curve, which is equal to $$e^y$$. From there I do $$\int_{0}^{2}\pi(e^{2y})dy -\int_{0}^{1}\pi(e^{2y})dy$$

 

[Mark44]

The region being revolved is bounded below by the line y = 1, above by the line y = 2, on the right by y = ln x, and on the left by the line x = 0. On your graph, this region has a roughly trapezoidal shape, and lies between the purple line and the light brown line. You first integral (it should include dy) gives you the volume of the rotated region.

BTW, you are integrating by using disks, not circles.

 

[HallsofIvy]

And the disks are horizontal, not vertical.

 

[warfreak131]

And the disks are horizontal, not vertical.

I meant that the disks are stacked on top of each other vertically.