I'm asked to determine if the following integral is convergent/divergent:

$\displaystyle \int_0^1 \ln(x) dx$

So I'm just wondering if I'm on the right track with what I'm doing:

$\displaystyle \int_0^1 \ln(x) dx = \lim_{t \rightarrow 0} \int_t^1 \ln(x) dx$

As $\displaystyle t \rightarrow 0 \Longrightarrow \ln(x) \rightarrow \infty$

So can I then just say this??:

$\displaystyle \int_0^1 \ln(x) dx = \infty \ \ \therefore \ \ \boxed{\mbox{Divergent}}$