How do you use the integral test to determine whether #int dx/lnx# converges or diverges from #[2,oo)#?
1 Answer
Jun 25, 2018
The integral
is divergent.
Explanation:
Note that in the interval
is:
1) Infinitesimal as
2) Positive as
3) Decreasing. In fact
4)
So, based on the integral test, the convergence of the integral:
is equivalent to the convergence of the series:
Now we can easily demonstrate that:
so that:
and as we know that the harmonic series:
is divergent, we can conclude that:
is divergent by direct comparison, and hence also:
is divergent.