Integration & Anti-derivatives - finding areas below graphs

 We have begun to define and use derivatives in physics, for things like defining velocity and acceleration as v = dx/dt and a = dv/dt. These are equivalent to finding the slopes of tangent lines on motion graphs, and being able to find instantaneous values of different quantities. We also have our rule/short cut for finding the derivatives once we know what the function looks like. 

This works great if we are given position, x(t), in a problem. But what if we are instead given acceleration, a(t), and need to work backwards to get velocity and position as functions of time??? We have to UNDO the derivatives to get those! We need some sort of ANTI-derivative. 

It turns out that ANTI-derivatives are used to find the AREAS below graphs, and that areas are often giving us useful information about an object or system. Check out this introduction to begin learning how this all works!