Chapter 6 of 10All chapters
Chapter 6 of 10
The link between them
Why one table of rules serves both.
They undo each other
Differentiating an accumulated total gives back the rate that produced it. That is the fundamental theorem of calculus, and it is what makes integrals computable rather than merely definable.
- It turns an infinite sum into a subtraction of two values.
- Without it, every integral would have to be approximated numerically.
An everyday picture
A car's odometer accumulates what the speedometer reads. Differentiate the odometer and you get the speedometer back; integrate the speedometer and you get the odometer.