# Infinte Area but finite Volume

1. Nov 11, 2004

### drcrabs

Whence evaluating the area under the curve

$$y=\frac{1}{x} \\\ \mbox{for} \\\ 1 \leq x < \infty$$

it evaluates to $$\infty$$

But when evaluating the volume using

$$Volume = \pi \int y^2 dx \\\ \mbox{on} \\\ a \leq x < b$$

hence

$$Volume = \pi \int \frac{1}{x^2} \\dx$$

hence

$$Volume = \pi [-\ \frac{1}{x}] \\\ \mbox{on} \\\ 1 \leq x < \infty$$

hence

$$Volume = \pi [0 - - 1] = \pi$$

A finite value!

Im having trouble comprehending such concepts and ideas.

Last edited: Nov 11, 2004
2. Nov 11, 2004