The homework question states:
Determine whether the infinite integral 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 .
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
You're right that .
What happens to the sine function as x tends to infinity?
Sine oscillates between -1 and 1...
How can you say what it converges to? You can't. Therefore it diverges...
You should be able to see the oscillatory behaviour in the graph... That's what it's asking for.