# Finding the volume of the integral

1. Jan 20, 2008

### sonzai

I need to find the volume of the solid obtained by rotating the region bounded by given curves about a specified line.
$$y = ln x, y = 1, y = 2, x = 0;$$ about the x-axis

since there are 3 "y"s
I'm not sure how to use
$$V = \int_{a}^{b} {A(x)}{dx}$$

2. Jan 20, 2008

### arildno

What you need to, is to find out how the cross-section actually looks like, for example by DRAWING it.

However, here's how you could proceed analytically:

Since for x<e, ln(x)<1, and will tend to negative infity as x trundles towards 0, it follows that this segment cannot be part of our region.

Thus, for 0<=x<=e, the cross-section lies between y=1 and y=2.

When x=e^2, ln(e^2)=2, so that for e<=x<=e^2, we have that our region lies between y=ln(x) and y=2.

Use this info to complete the problem.