The homework question states:

Determine whether the infinite integral $\displaystyle \int_{1}^{\infty}\frac{1}{x}cos(lnx) dx$ converges or diverges. Explain the outcome of your calculation, using a

*sketch* (representing a domain of the form [1,a] for a suitable large value a) of the graph of $\displaystyle sin(lnx)$.

My question(s):

How does a graph help explain, better put, what am I looking for in this graph and how am I supposed to use it? (I've read my notes over and over, but they still make no sense...)

I understand that the integral = sin(ln(x))....

With regards to [1,a], isn't a=lower bound of the integral? i.e. a=1?

Thanks in advance

tsal15