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.