- #1

mrdoe

- 36

- 0

**Paradox? An infinite set having finite volume??**

## Homework Statement

Find the volume, in terms of k, of the solid made from R rotating about the y-axis, if R is defined as the region bounded by [tex]e^{-x}[/tex] and the coordinate axes.

**2. The attempt at a solution**

Obviously, [tex]\displaystyle\int^{1}_{0} (\ln (y))^2\pi dx = [/tex] undefined... but the region R itself has a finite volume. So if you rotate it shouldn't it have a finite volume?