Brainlet here -
Question regrading logic/reason/purpose of calculating derivitives and integration of line/curve to test data.
I run a car acceleration test, collection data - time, distance, speed.
I plot the data, fit a line/curve, to it, its exponential.
From the curve fit to data to data points, I can determine forumula of the curve
then calculate values in between data points. From the curve I can calculate
distance, velocity, and acceleration (take derivitive of line at a particular point) at any point along the line
and project beyond the data set.
But, I am not clear on why a person would integrate the curve formula to get the area under the curve?
I have some understanding of the relationship between integration and derivitives, but a
deep understanding of the relationship, and actual application of concepts to real test data.
Where can I find a good explanation of these concepts and examples of application of these concepts?
At uni the instructors just read from the book, taught to the book. Every time I asked "why"
the instructors just gave the brain dead procedural answer. I do not think they actually understood
why or how to actually apply the concepts, or if they reviewed the application of the concepts by someone
else they would not identify the concepts were applied incorrectly if the procedures were correct.

I know this is an over simple example, but I want to be sure I better understand the simple application, then move to
apply the concept to analyzing pressure buildup and falloff testing for wells where the exponetial integral is used,
and better understand why integration is being used to develop the formula used to evalute the test data, if this makes
sense.