If someone asks me : what have you been doing this afternoon and I want to say that I have been reading the newspaper, emphasizing the activity, how I have been occupying myself, not the result, even though I have finished reading the entire paper, can I use the perfect progressive or do I have to use the present perfect: What have you been doing? I have read the paper/ I have been reading the paper?
The progressive or continuous indicates ongoingness or repetition.
I've been repairing the shed's roof this afternoon.
does not mean that the shed is now repaired, only that you have bee doing something towards the repair, whereas
I've repaired the shed's roof.
indicates that the shed's roof is now ready to be rained on.
P.S. Let's take a real world situation.
If you are asked
What have you been doing all afternoon?
if would be improper to reply
I have brushed my teeth.
since the question wants either a single activity that occupied you throughout the afternoon, or a list of the activities which have occupied you.
So, you could say, in response to the question "What have you been doing":
I have brushed my teeth and I have paid a few bills and I have given the dog a bath.
I have been playing FIFA.
If you say
I have been brushing my teeth all afternoon.
people will think you have an obsessive-compulsive disorder.
Question: What have you been doing [up to the point where I am asking you this question].
- I've been reading the paper. [up until this point in time in the present].
Question: What have you done this afternoon?
- I've read the paper. OR I read the paper. Either is fine.
The first is general and merely states it was in the past without any more information.
The second is more specific and implies a specific act that is finished.
In practical terms, they are both acceptable.