Where you meet it

Beyond the classroom.

In work

Machine learning optimises with gradients. Graphics use curves and surfaces. Finance prices change over time. Engineering integrates loads. Epidemiology models spread.

You will rarely compute an integral by hand after school.
You will regularly need to know what a rate and a total mean.

The takeaway

If you remember only two things: a derivative is how fast something is changing right now, and an integral is how much has piled up. Nearly every application is one of those two questions.