find the length of the curve y = 1/x on the interval [0, ∞)?

Question

rulnick · Answer

It's infinite.

anonymous · Answer

how do you prove it diverges

rulnick · Answer

The curve 1/x only asymptotically approaches the y and x axes.  Graphically it is obvious.  Are you required to make an algebraic argument with the line integral for divergence?  Or is the graphical argument sufficient?

anonymous · Answer

yea required algebraic argument

anonymous · Answer

but i can see why its infinite on the graph

rulnick · Answer

This might be difficult to convey here.  Let me see if I can come up with something.

anonymous · Answer

if not then its ok.

anonymous · Answer

dont waste your time on it thank you

rulnick · Answer

Thanks for the medal.  I hope this will help:

The length of the curve would be integral from 0 to infinity of sqrt(1-x^(-2)) dx.

rulnick · Answer

This integral is a bit of a mess, but it works out to

Kx - atan(Kx)

where

K = sqrt(1-x^(-2)).