# Numerical Integration:

## Accumulating Rates of Change

The fundamental theorem of calculus tells us that if we know the rate of change of some quantity, then adding up (or integrating) the rate of change over some interval will give the total change in that quantity over the same interval. For example, if a car is moving along a straight line and we know the speed of the car as a function of time, it is possible to determine the total change in the car's position over some time interval. But what if we don't know a formula for the car's velocity, but we only have measured its velocity at certain instants of time? Is it possible to "integrate" this discrete data in order to estimate the change in the car's position? If so, how?

In this interactive Web application, we provide a mechanism for choosing from among five different numerical schemes for integrating experimental data. In the Numerical Integration Lab you can learn the mathematical ideas behind modeling functions that produce experimental data. By integrating the model, we approximate the (true) integral of the underlying (unknown) function.

The Geometry Center Calculus Development Team