It’s not. You can’t define it to be whatever you want just to suit the fact that the idiom is used incorrectly. A learning curve is a graph of knowledge acquired vs. time.
Wikipedia:
A learning curve is a graphical representation of the changing rate of learning (in the average person) for a given activity or tool. Typically, the increase in retention of information is sharpest after the initial attempts, and then gradually evens out, meaning that less and less new information is retained after each repetition.
Means that you could graph knowledge against the sum-total of the effort -- that is the 'work' x repetitions -- this is equivalent to the integral of what you described... which is *STILL* a graphical representation of the items in question (though indirect), just as the derivative would be a graphical representation thereof (readily showing the changes in the learning rate) -- all three functions show the same underlying data, just with different aspects readily visually accessible.