/sci/ - Science & Math

>>10307877
(continued)
I forgot to mention that f(c[i])*(x[i] - x[i - 1]) represents the distance traveled during the interval [x(i - 1), x(i)] because f(c[i]) represents a velocity while (x[i] - x[i - 1]) represents time, so of course their product is the distance.

So Integral Calculus tells you how a quantity accumulates over time when you have a function which describes the rate of change of that quantity over time. Conversely, if you have a function which describes how a quantity accumulates over time, you can use Differential Calculus to find the rate of change of that quantity over time (this is actually easier to understand than integration so I won't bother with a detailed explanation).

So integration and differentiation are inverse operators on functions and they allow you to understand the behaviour of functions and that can be useful in a variety of fields from physics to economics.