I am writing an essay for my calculus class and one of the requirements to meet within the essay is to demonstrate an understanding of integration by explaining a metaphor that uses integration.
This is the passage that I think meets that requirement but I am not sure if I should expand more on integration just to be sure:
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 conjures this reminiscent math memory to 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 required to be summed to get an exact measurement of area under a curve. Despite the impossibility of calculating an infinite amount of something we must still calculate some amount of it if we wish to obtain the valuable information an approximation can provide.
For reference, here is the metaphor I am writing about:
"The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous. To understand the laws of this continuous movement is the aim of history. . . . Only by taking inﬁnitesimally small units for observation (the diﬀerential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, ﬁnding the sum of these inﬁnitesimals) can we hope to arrive at the laws of history"
Could anyone provide some feedback? thanks!