I can't say exactly what application it is. At first, total differential and integral originated from the solution of physical problems.

For example, the relationship between distance, velocity and acceleration is the relationship between derivative and integral. The first derivative of the equation of distance versus time is the equation of velocity versus time, and the second derivative is the equation of acceleration versus time.

I think almost all derivatives and integrals in high school can be used in physics.

The convenience of derivative and integral lies in the following situations.

If you know the changing law of a changing speed over a period of time, so that you can find out the distance traveled, then you can directly use the integral to solve it.