Integration in Physics

Lets say you want to calculate P(t)=P(0)+ P'(t)*dt you would usually do a simple integration over t on some interval. But this assumes that the step dt is infinitly small. In a computer simulation dt has to be approximated by some small number (since the computer only got finite precision), which means that we can only approximate the end result.

The simplest form of numerical integration is Euler integration:
dt = Tn - Tn-1
P(Tn) = P(Tn-1) + P'(Tn-1)*dt

But this will end up with different result depending on how large dt is. Smaller steps will yield better results, but take longer time or demand higher precision.

There are an article here on Gamedev about numerical integration, which could help you. It discusses euler and other methods for integrating.
http://www.gamedev.net/reference/programming/features/verlet/

It's probably describes it better than this attempt =)

Treat the integral as a summation over a finite number of tiny intervals, rather than an infinite number of infintitely small intervals. You must discretize the otherwise continuous function.

Integration Basics

Quote:

Original post by GaryNas What does the term "numerical integration" mean in terms of a physics engine?

Estimation of a future position.

You know when you have speed of "a" and accleration of "b" and you'd need to know your future position.