Question

Does this passage reflect an understanding of integration: To a person familiar with integration attempting to relate the metaphor back to math, this statement likely brings to mind images of their first calculus instructor drawing rectangles below a function when showing the class how to calculate the area under a curve.
The reason Tolstoy’s statement likely brings this reminiscent math memory to mind is because the two concepts being discussed are abstractly identical. Just as the wills of man that direct the compass of history are innumerable, so are the number of rectangles that are req

Answer 1

required to be summed to get an exact measurement of area under a curve.

Answer 2

Its an essay for a calc class

Answer 3

I think it does.

Answer 4

Now that I read it twice, I'm sure it does. He talks about Riemann sums, which basically is what an integral is; you sum up an infinite amount of infinitely small rectangles.

Answer 5

This from War and Peace, right? Maybe you could provide the reference in your essay.

It's an interesting analogy, I'm not entirely sure how far it can be taken but yes, I would say that the person (Tolstoy) making the analogy has an understanding of integration as a process of summation.

Answer 6

Ok, but the question I am asking is if the paragraph (above) explaining how Tolstoy's metaphor is related to integration shows an understanding of integration. I am trying to decide whether I should expand on it.

Answer 7

I think it is sufficient, I would perhaps replace "calculate" with "approximate" since it is physically impossible to draw an infinite number of infinitesimally thin rectangles.