is the integral of 1/x defined on [0,1]?

Question

i know its an improper integral, but i ended up with:

lim ln 1 - ln a (as a approaches zero)

and i'm pretty sure that doesn't exist. help?

Answer 1

continuing the expression yields ln (1/a); so as a approaches zero, the ln approaches infinity, therefore integral does not exist

Answer 2

Hey there!

You are right. The real value of ln 0 is - infinity. So the improper integral will diverge, as the limit approaches infinity. So the limit does not exist.

Hope it helps!

Answer 3

You are right. ln(0) is undefined, so the integral from 0 to1 is undefined.