Math Forum Discussions

Steven

Posts: 210
Registered: 12/10/04

real analysis question
Posted: Aug 6, 2012 10:39 PM

Plain Text

I read a theorem that states if f is unbounded on [a,b] then it is not integrable (riemann)on [a,b].
I guess I do not know what it is saying because I simply do not agree with the statement of the theorem. There are many unbounded functions which are integrable. This is a standard topic in calculus--whether an unbounded function over an interval converges or not. Consider int(ln x)dx from 0 to 1. Ln x is not bnd from below yet this integral converges to -1. How about the int (arctan x)dx from -pi/2 to pi/2. It is not bnd from below or above and it converges.
What am I missing??????????????
Thank you,
Steven